Inclusion Criteria:

• Participants is able to provide written informed consent (participant, parent or legal guardian, and, as appropriate, participant assent) to participate in the study before completing any study-related procedures.
• Participant is male or female aged 11-55 years, inclusive, at time of consent.
• Participant has histologic evidence of eosinophilic esophagitis (EoE) with a peak eosinophil count of greater than or equal to (>=) 15/ high-powered field (HPF), from 2 of 3 (proximal, mid-, and/or distal) levels of the esophagus at the screening endoscopy.
• Participant has a history of clinical symptoms of esophageal dysfunction (for example, eating problems, abdominal pain, heartburn, dysphagia, vomiting, food impaction, weight loss) intermittently or continuously at screening (Visit -1).
• Participants must have experienced dysphagia (response of "yes" to question 2 on Dysphagia Symptom Questionnaire [DSQ]) on a minimum of 4 days and completed the DSQ on >= 70 percent (%) of days in any 2 consecutive weeks of the screening period and in the last 2 weeks prior to the baseline visit (Visit 1).
• Participant must not have PPI-responsive EoE based on esophageal biopsies performed after the patient has been on at least 8 weeks of high-dose PPI therapy (high-dose therapy refers to the total daily dose, which may have been administered as a once or twice daily dosing regimen). This may occur at the time of the qualifying esophagogastroduodenoscopy (EGD) (in which case the same proton pump inhibitor (PPI) regimen must be continued), or this may have been done previously (in which case PPI therapy may have been stopped if there was no response to therapy based on esophageal biopsy results). If PPI responsiveness was excluded by a previous EGD and biopsy, the historical EGD and biopsy must have been performed after the patient had been on a minimum of 6 weeks of high-dose PPI therapy.
• Participant will be on a stable (no changes) diet >=3 months prior to the screening visit (Visit -1).
• Participant is willing and able to continue any dietary therapy, environmental therapy, and/or medical regimens (including gastric acid suppression) in effect at the screening visit (Visit -1). There should be no change to these regimens during study participation.
• All female participants must have a negative serum pregnancy test (beta-human chorionic gonadotropin [β-hCG]) prior to enrollment into the study. Females of childbearing potential must agree to continue acceptable birth control measures (for example, abstinence, stable oral contraceptives, or double-barrier methods) throughout study participation.
• Participant is willing and has an understanding and ability to fully comply with study procedures and restrictions defined in this protocol.

Exclusion Criteria:

• Participant has any condition or abnormality (including laboratory abnormalities), current or past, that, in the opinion of the principal investigator or medical monitor, would compromise the safety of the participant or interfere with or complicate the assessment of signs or symptoms of EoE. Such conditions may include psychiatric problems; neurologic deficits or disease; developmental delay; cardiovascular, metabolic, or pulmonary disease; or previous gastroesophageal surgery. These should be discussed with the medical monitor.
• Participant has used immunomodulatory therapy within 8 weeks prior to the qualifying EGD or between the qualifying EGD and baseline visit (Visit 1) or anticipates using immunomodulatory therapy during the treatment period (except for any ongoing regimen of allergy shots). Use of long-acting immunomodulatory therapy (for example, Rituxan) within 3 months of the qualifying EGD should be reviewed with the medical monitor.
• Participant has been using swallowed topical corticosteroid for EoE or systemic corticosteroid for any condition within the 4 weeks prior to the qualifying EGD, between the qualifying EGD and baseline visit (Visit 1), or anticipates use during the treatment period; any temporary use (less than or equal to [<=]7 days) or initiation of new steroid treatment during the study should be documented and discussed with the medical monitor prospectively but cannot occur within 4 weeks of the final EGD.
• Participant has been on inhaled steroids and has not been on stable treatment for >=3 months prior to screening visit (Visit -1). Participants on inhaled steroids need to stay on a stable treatment during study participation. Participant has been on intranasal steroids and has not been on stable treatment for a minimum of 4 weeks prior to the qualifying EGD. After the qualifying EGD, participants with seasonal allergic rhinitis may resume (or discontinue) intranasal corticosteroids based on the participant's usual treatment regimen for allergy season.
• Participant has initiated, discontinued, or changed dosage regimen of PPIs, H2 antagonists, antacids, or leukotriene inhibitors for any condition (such as gastroesophageal reflux disease, asthma or allergic rhinitis) within the 4 weeks prior to the qualifying EGD, between the qualifying EGD and baseline visit (Visit 1), or anticipates changes in the use of such medications during the treatment period.
• Participant has been using cytochrome P450 3A4 (CYP450 3A4) inhibitors (for example, ketoconazole, grapefruit juice) within the 2 weeks prior to the baseline visit (Visit 1) or within 5 half-lives (whichever is greater) or anticipates using such medications during the treatment period.
• Participant has an appearance on qualifying EGD of an esophageal stricture (high-grade), as defined by the presence of a lesion that does not allow passage of a diagnostic adult upper endoscope (for example, with an insertion tube diameter of greater than [>]9 millimeter [mm]).
• Participant is on a pure liquid diet or the 6-food elimination diet.
• Participant has had an esophageal dilation within the 3 months prior to screening (Visit -1).
• Participant has presence of esophageal varices at the screening endoscopy.
• Participant has any current disease of the gastrointestinal tract, aside from EoE, including eosinophilic gastritis, enteritis, colitis, or proctitis; inflammatory bowel disease; or celiac disease.
• Participant has other diseases causing or associated with EoE, including hypereosinophilic syndrome, collagen vascular disease, vasculitis, achalasia, or parasitic infection.
• Participant has current evidence of oropharyngeal or esophageal candidiasis.
• Participant has a potentially serious acute or chronic viral infection or immunodeficiency condition, including tuberculosis, fungal, bacterial, viral/parasite infection, ocular herpes simplex, herpes esophagitis, or chicken pox/measles.
• Participant has upper gastrointestinal bleeding within 4 weeks prior to the screening visit (Visit - 1) or between the screening visit and baseline visit (Visit 1).
• Participant has evidence of active infection with Helicobacter pylori.
• Participant has evidence of unstable asthma within 4 weeks prior to the screening visit (Visit -1) and between the screening visit and baseline visit (Visit 1).
• Participant is female and pregnant or nursing.
• Participant has a history of intolerance, hypersensitivity, or idiosyncratic reaction to budesonide (or any other corticosteroids) or to any other ingredients of the investigational product.
• Participant has taken part and received intervention in an interventional study related to EoE (except for an interventional study for a topical swallowed steroid) within 6 months prior to the screening visit (Visit -1), or any investigational study within 30 days prior to the screening visit (Visit -1). An investigational topical swallowed steroid must have been discontinued at least 30 days prior to the screening visit (Visit -1).
• Participant has a history or high risk of noncompliance with treatment or regular clinic visits.
• Participant has previously completed, discontinued, or withdrawn from this study.
• Participant has participated in a previous clinical study involving oral budesonide suspension (OBS) (SHP621).
• Participant anticipates using sucralfate during the study.