Inclusion Criteria

1. Satisfy the 2016 American College of Rheumatology/European League Against Rheumatism criteria for the classification of SjS at screening (score ≥ 4), and who have disease duration (from time of initial clinical SjS diagnosis) of at least 16 weeks prior to screening.
2. Have moderate to severe SjS ESSDAI ≥ 5.
3. Short duration of disease (≤ 10 years) before screening.
4. A stimulated whole salivary flow (SWSF) ≥ 0.05 mililiters/minute (mL/minute).
5. Positive anti-Sjögren's syndrome-associated antigen A (anti-Ro/SSA) at screening.

Exclusion Criteria

1. Autoimmune disease other than SjS (for example, rheumatoid arthritis, systemic lupus erthrematosus [SLE], systemic sclerosis).
2. Active fibromyalgia with pain symptoms or signs that would interfere with joint assessment or requiring adjustment in medication within the 3 months before screening to control symptoms; participants with fibromyalgia that is well controlled on stable treatment may otherwise be considered.
3. Medical condition associated with sicca syndrome.
4. Previous exposure to tyrosine kinase 2 (TYK2) inhibitors such as deucravacitinib or related compounds.

* Other protocol-defined Inclusion/Exclusion criteria apply.