• Have a definite diagnosis of RRMS, as per the revised McDonald 2010 criteria
• Have a length of disease duration, from first documented clinical attack consistent with MS disease of less than or equal to (</=) 3 years
• Within the last 12 months one or more clinically reported relapse(s) or one or more signs of MRI activity
• EDSS of 0.0 to 3.5 inclusive, at screening
• An agreement to use an acceptable birth control method for women of childbearing potential, during the treatment period and for at least 6 months or longer after the last dose of study drug

Exclusion Criteria:

• Secondary progressive multiple sclerosis or history of primary progressive or progressive relapsing MS
• Inability to complete an MRI
• Known presence of other neurological disorders

Exclusions Related to General Health:

• Pregnancy or lactation
• Participants intending to become pregnant during the study or within 6 months after the last dose of the study drug
• Any concomitant disease that may require chronic treatment with systemic corticosteroids or immunosuppressants during the course of the study
• History or currently active primary or secondary immunodeficiency
• Lack of peripheral venous access
• History of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibodies
• Significant or uncontrolled somatic disease or any other significant disease that may preclude participant from participating in the study
• Congestive heart failure (New York Heart Association III or IV functional severity)
• Known active bacterial, viral, fungal, mycobacterial infection or other infection, (excluding fungal infection of nail beds) or any major episode of infection requiring hospitalization or treatment with IV antibiotics within 4 weeks prior to screening or oral antibiotics 2 weeks prior to screening
• History of malignancy, major opportunistic infections, alcohol or drug abuse, recurrent or chronic infection, and/or coagulation disorders

Exclusions Related to Medications:

• Received any prior approved disease modifying treatment (DMT) with a label for MS, for example, interferons, glatiramer acetate, natalizumab, alemtuzumab, daclizumab, fingolimod, teiflunomide and dimethylfumarate
• Receipt of a live vaccine or attenuated live vaccine within 6 weeks prior to the baseline visit
• Previous treatment with B-cell targeted therapies (i.e., rituximab, ocrelizumab, atacicept, belimumab, or ofatumumab)
• Any previous treatment with immunosuppressants/ immunomodulators/ antineoplastic therapies (cyclophosphamide, azathioprine, mycophenolate mofetil, cyclosporine, methotrexate, cladribine, mitoxantrone, laquinimod, total body irradiation, or bone marrow transplantation)
• Treatment with investigational DMT
• Treatment with fampridine/dalfamipridine unless on stable dose for >/=30 days prior to screening

Exclusion related to Shorter Infusion Substudy:

- Any previous serious IRRs experienced with ocrelizumab treatment