Inclusion Criteria:  Male participants with histologically- or cytologically-confirmed adenocarcinoma of the prostate without small cell histology Has metastatic disease assessed by investigator and verified by BICR by either ≥2 bone lesions on bone scan and/or visceral disease by computed tomography/magnetic resonance imaging (CT/MRI) Willing to maintain continuous ADT with a LHRH agonists or antagonists during study treatment or have a history of bilateral orchiectomy Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 assessed within 10 days of randomization Participants receiving bone resorptive therapy (including, but not limited to, bisphosphonate or denosumab) must have been on stable doses prior to randomization Has adequate organ function Has provided newly obtained core or excisional biopsy (obtained within 12 months of screening) from soft tissue not previously irradiated (samples from tumors progressing in a prior site of radiation are allowed). Participants with bone only or bone predominant disease may provide a bone biopsy sample Male participants must agree to the following during the intervention period and for at least 120 days after the last dose of study intervention: Refrain from donating sperm PLUS either be abstinent from heterosexual intercourse and agree to remain abstinent OR agree to use contraception, unless confirmed to be azoospermic Male participants must agree to use male condom when engaging in any activity that allows for passage of ejaculate to another person of any sex  Exclusion Criteria:  Has a known additional malignancy that is progressing or has required active treatment in the last 3 years Has an active autoimmune disease that has required systemic treatment in past 2 years Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy Has undergone major surgery including local prostate intervention (excluding prostate biopsy) within 28 days prior to randomization and not recovered adequately from the toxicities and/or complications Has a gastrointestinal disorder affecting absorption or is unable to swallow tablets/capsules Has an active infection (including tuberculosis) requiring systemic therapy Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis Has known active human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV) infection Has known or suspected central nervous system (CNS) metastases and/or carcinomatous meningitis Has a history of seizure or any condition that may predispose to seizure Has a history of loss of consciousness within 12 months of screening Has had myocardial infarction or uncontrolled angina within 6 months prior to randomization, or has New York Heart Association class III or IV congestive heart failure or a history of New York Heart Association class III or IV congestive heart failure Has hypotension (systolic blood pressure <86 millimeters of mercury [mmHg]) or uncontrolled hypertension (systolic blood pressure >170 mmHg or diastolic blood pressure >105 mmHg) at the screening visit Has a history of clinically significant ventricular arrhythmias Has hypersensitivity to pembrolizumab and/or enzalutamide and/or any of their excipients Has received prior ADT as neoadjuvant/adjuvant therapy for non-metastatic prostate cancer for >39 months in duration or within 9 months prior to randomization or with evidence of disease progression while receiving ADT Has had prior treatment with a next generation hormonal agent (eg, abiraterone, enzalutamide, apalutamide, darolutamide) Has received prior therapy with an anti-programmed cell death-1 (anti-PD-1), anti-programmed cell death-ligand 1 (anti-PD-L1), or anti PD-L2 agent or with an agent directed to another stimulatory or coinhibitory T-cell receptor Has received a live vaccine within 30 days prior to randomization Has a "superscan" bone scan Has had an allogenic tissue/solid organ transplant Is expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of study treatment  Has received any prior pharmacotherapy, radiation therapy or surgery for metastatic prostate cancer with the following exceptions:  Up to 3 months of ADT or orchiectomy with or without concurrent first-generation antiandrogens, if patient was not treated with docetaxel May have 1 course of palliative radiation or surgical therapy to treat symptoms resulting from metastatic disease if it was administered at least 4 weeks prior to randomization For participants with low volume metastatic disease, may have 1 course of definitive radiotherapy if it was administered at least 4 weeks prior to randomization Up to 6 cycles of docetaxel therapy with final treatment administration completed within 2 months of randomization and no evidence of disease progression. In these participants up to 6 months of ADT permitted