A Study to Evaluate the Efficacy, Safety, Pharmacokinetics (PK), and Pharmacodynamics (PD) of Satralizumab in Participants With Anti-N-methyl-D-aspartic Acid Receptor (NMDAR) or Anti-leucine-rich Glioma-inactivated 1 (LGI1) Encephalitis

Inclusion Criteria: * Reasonable exclusion of tumor or malignancy before baseline visit (randomization) * Onset of AIE symptoms ≤ 9 months before randomization * Meet the definition of "New Onset" or "Incomplete Responder" AIE * For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use adequate contraception during the treatment period and for at least 3 months after the final dose of satralizumab or placebo * For participants enrolled in the extended China enrollment phase at China's sites: participants who are current residents of mainland China, Hong Kong, or Taiwan, and of Chinese ancestry NMDAR AIE Cohort: * Age ≥ 12 years * Diagnosis of probable or definite NMDAR encephalitis LGI1 AIE Cohort * Age ≥ 18 years * Diagnosis of LGI1 encephalitis Exclusion Criteria: * Any untreated teratoma or thymoma at baseline visit (randomization) * History of carcinoma or malignancy, unless deemed cured by adequate treatment with no evidence of recurrence for ≥ 5 years before screening * For participants with NMDAR AIE, history of negative anti-NMDAR antibody in cerebrospinal fluid (CSF) using a cell-based assay within 9 months of symptom onset * Historically known positivity to an intracellular antigen with high cancer association or glutamate decarboxylase 65 (GAD-65) * Historically known positivity to any cell surface neuronal antibodies other than NMDAR and LGI1, in the absence of NMDAR and LGI1 antibody positivity * Confirmed paraneoplastic encephalitis * Confirmed central or peripheral nervous system demyelinating disease * Alternative causes of associated symptoms * History of herpes simplex virus encephalitis in the previous 24 weeks * Any previous/concurrent treatment with interleukin-6 (IL-6) inhibitory therapy (e.g., tocilizumab), alemtuzumab, total body irradiation, or bone marrow transplantation * Any previous treatment with anti-cluster of differentiation 19 antibody (CD19 antibody), complement inhibitors, neonatal Fc receptor antagonists, anti-B-lymphocyte stimulator monoclonal antibody * Any previous treatment with T-cell depleting therapies, cladribine, or mitoxantrone * Treatment with oral cyclophosphamide within 1 year prior to baseline * Treatment with any investigational drug (including bortezomib) within 24 weeks prior to screening * Concurrent use of more than one immunosuppressive therapy (IST) as background therapy * Contraindication to all of the following rescue treatments: rituximab, intravenous immunoglobulin (IVIG), high-dose corticosteroids, or intravenous (IV) cyclophosphamide * Any surgical procedure, except laparoscopic surgery or minor surgeries within 4 weeks prior to baseline, excluding surgery for thymoma or teratoma removal * Planned surgical procedure during the study * Evidence of progressive multifocal leukoencephalopathy * Evidence of serious uncontrolled concomitant diseases * Congenital or acquired immunodeficiency, including human immunodeficiency virus (HIV) infection * Active or presence of recurrent bacterial, viral, fungal, mycobacterial infection, or other infection * Infection requiring hospitalization or treatment with IV anti-infective agents within 4 weeks prior to baseline visit * Positive hepatitis B (HBV) and hepatitis C (HCV) test at screening * Evidence of latent or active tuberculosis (TB) * History of drug or alcohol abuse within 1 year prior to baseline * History of diverticulitis or concurrent severe gastrointestinal (GI) disorders that, in the investigator's opinion, may lead to increased risk of complications such as GI perforation * Receipt of live or live-attenuated vaccine within 6 weeks prior to baseline visit * History of blood donation (1 unit or more), plasma donation or platelet donation within 90 days prior to screening * History of severe allergic reaction to a biologic agent * History of suicide attempt within 3 years prior to screening except if this is clearly associated with and occurs during the acute phase of LGI-1 or NMDAR encephalitis * Any serious medical condition or abnormality in clinical laboratory tests that, in the investigator's judgment, precludes safe participation in and completion of the study * Pregnant or breastfeeding, or intending to become pregnant during the study or within 3 months after the final dose of study drug