Inclusion Criteria:

• Has histologically confirmed epithelial ovarian cancer, fallopian tube cancer or primary peritoneal cancer
• Has received a front line platinum-based regimen (administered via either intravenous or intraperitoneal route) per local standard of care or treatment guideline following the primary or interval debulking surgery with documented disease recurrence
  • Maintenance treatment following the front line treatment is permitted and counted together as part of the front line treatment
• Has fulfilled the following additional requirements regarding prior treatments for recurrent ovarian cancer (ROC) depending on the cohort participant is to be enrolled
  • Each participant must have documented evidence of clinical response or disease stabilization to the last regimen received
  • Cohort A
    • Has received 0 to 2 additional prior lines for treating ROC (or 1-3 total prior lines counting the front line)
    • Must have a platinum-free interval (PFI) of ≥ 3 to 12 months if the last regimen received is a platinum-based, or a treatment-free interval (TFI) of ≥ 3 to 12 months if the last regimen received is non-platinum-based
  • Cohort B
    • Has received 3 to 5 additional prior lines for treating ROC (or 4-6 total prior lines counting the front line)
    • Must have a PFI of ≥ 3 months if the last regimen received is a platinum-based, or a TFI of ≥ 3 months if the last regimen received is a non-platinum-based
• Has measurable disease at baseline based on Response Evaluation Criteria is Solid Tumors (RECIST) 1.1 as determined by the central imaging vendor
• Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
• Has a life expectancy of ≥16 weeks
• Has provided a tumor tissue sample either collected from prior cytoreductive surgery or fresh newly obtained tumor tissue at screening
• Has adequate organ function
• Female participants of childbearing potential must be willing to use an adequate method of contraception for the course of the study through 120 days after the last dose of study drug

Exclusion Criteria:

• Is currently participating in or has participated in a clinical study and received an investigational agent or used an investigational device within 4 weeks prior to the first dose of study treatment
• Has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., use of disease modifying agents, corticosteroids or immunosuppressive drugs)
  • Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment
• Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the planned first dose of the study
• Has had prior anti-cancer monoclonal antibody (mAb), chemotherapy, targeted small molecule therapy, or radiation therapy within 4 weeks prior to the planned first dose of the study
• Has not recovered from adverse events to ≤ Grade 1 or prior treatment level due to a previously administered agent
• Has epithelial ovarian cancer (EOC) with mucinous histology subtype
• Has a known additional malignancy that progressed or required active treatment within the last 5 years
  • Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer
• Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis
  • Participants with previously treated brain metastases may participate provided they have stable brain metastases
• Has known history of, or any evidence of active, non-infectious pneumonitis
• Has an active infection requiring systemic therapy
• Has symptoms of bowel obstruction in the past 3 months
• Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study
• Is pregnant or breastfeeding, or expecting to conceive children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of study drug
• Has received prior therapy with an anti-programmed cell death (PD)-1, anti-PD-ligand-1 (anti-PD-L1), anti-PD-L2 agent or with an agent directed to another co-inhibitory T-cell receptor (e.g. cytotoxic T-lymphocyte-associated antigen-4 [CTLA-4], tumor necrosis factor receptors OX-40 or CD137) 
• Has participated in prior pembrolizumab (MK-3475) studies
• Has a known history of Human Immunodeficiency Virus (HIV)
• Has known active Hepatitis B or Hepatitis C
• Has received a live vaccine within 30 days of the planned first dose of the study