Inclusion Criteria:

* Medically stable on the basis of physical examination, medical history, vital signs, 12-lead electrocardiogram (ECG) and clinical laboratory tests performed at screening
* Meets criteria for diagnosis of SjD by the 2016 American College of Rheumatology/European Alliance of Associations for Rheumatology (ACR/EULAR) classification criteria
* Seropositive for antibodies to Ro/SSA at screening
* Total ClinESSDAI score greater than or equal to (>=) 5 at screening
* Participants of childbearing potential must have a negative highly sensitive serum (beta-hCG) pregnancy test at screening and a negative urine pregnancy test at Week 0 prior to randomization

Exclusion Criteria:

* Has a history of severe, progressive and/or uncontrolled hepatic, gastrointestinal, renal, pulmonary, cardiovascular, psychiatric, neurological or musculoskeletal disorder, hypertension, and/or any other medical or uncontrolled autoimmune disorder or clinically significant abnormalities in screening laboratory
* Known allergies, hypersensitivity, or intolerance to nipocalimab or its excipients or excipients used in the placebo formulation
* Has any confirmed or suspected clinical immunodeficiency syndrome not related to treatment of his/her SjD or has a family history of congenital or hereditary immunodeficiency
* Has shown a previous severe immediate hypersensitivity reaction, such as anaphylaxis, to therapeutic proteins (for example [e.g.], monoclonal antibodies, intravenous immunoglobulin)
* Has any unstable or progressive manifestation of SjD that is likely to warrant escalation in therapy beyond permitted background medications