For more information regarding Bristol-Myers Squibb Clinical Trial participation, please visit www.BMSStudyConnect.com Inclusion Criteria: - Pathologically confirmed PCNSL or PTL who failed or did not respond to at least 1 line of systemic therapy - Measurable disease requirements on scans: PCNSL subjects should have at least one measurable extranodal brain lesion; PTL subjects should have at least 1 measurable extranodal lesion or nodal lesion - Have tumor tissue for PD-L1 expression testing - Must have a Karnofsky performance status of 70-100 Exclusion Criteria: - a) Intraocular PCNSL without evidence of brain disease b) PCNSL patients who cannot undergo MRI assessments c) PCNSL patients with systemic disease - Patients with certain diseases such as active autoimmune disease, type I diabetes, hypothyroidism that needs hormone replacement, active infection, psychiatric disorder - Prior malignancy active within the previous 3 years except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the prostate, cervix, or breast - Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways PCNSL, and PTL subjects with brain or spinal cord lesion who have received doses of more than 2 mg/day of dexamethasone or equivalent within the 14 days period prior to the first dose of nivolumab are excluded Other protocol defined inclusion/exclusion criteria could apply