Inclusion Criteria:
* Age greater than equal to (\>=)18 years OR of legal age of consent in the jurisdiction in which the study is taking place, at the time of signing the Informed Consent Form.
* Confirmed diagnosis of clinical VEXAS defined by:
1. Documented evidence of a canonical, pathogenic Ubiquitin-like modifier activating enzyme 1 (UBA1) mutation
2. Inflammatory manifestations: current or documented past involvement within 6 months of at least one organ system
* Receiving glucocorticoid (GC) treatment (prednisone/prednisolone) for \>=4 consecutive weeks for \>=10 days prior to randomization.
* A female participant is eligible to participate if she is not pregnant or breastfeeding and one of the following conditions applies:
1. Is a Participant of non-childbearing potential (PONCBP) OR
2. Is a Participant of childbearing potential (POCBP) and using a contraceptive method that is highly effective
* Is capable of giving signed informed consent including compliance with the requirements and restrictions
* Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0 to 2 at the time of screening.
* Has adequate organ function
Exclusion Criteria:
* More than 1 prior admission to an intensive care unit due to a VEXAS flare within the 6 months prior to randomization.
* History of severe corticosteroid toxicity: uncontrolled concomitant cardiovascular, nervous system, pulmonary (including obstructive pulmonary disease), renal, hepatic, endocrine (including uncontrolled diabetes mellitus), psychiatric, osteoporosis/osteomalacia, glaucoma, corneal ulcers/injuries, nausea or vomiting or gastrointestinal disease.
* High risk/very high risk Myelodysplastic syndrome (MDS), according to the Revised International Prognostic Scoring System (IPSS-R) with overall risk score \>3.5.
* Peripheral blood blast counts \>=10%.
* Multiple myeloma (all stages) and other active plasma cell dyscrasias requiring treatment.
* Malignancy (except disease under study including Lower-risk myelodysplastic syndrome \[LR-MDS\]) that has progressed or required active treatment within the past (24 months) except for basal cell or squamous cell carcinomas of the skin or in-situ carcinomas).
* Uncontrolled intercurrent illness within 12 weeks prior to initiation of momelotinib.
* Ongoing adverse reaction(s) from prior therapy that have not recovered to Grade \<=1 per NCI CTCAE v6.0 or to the Baseline status preceding prior therapy
* Psychiatric illness, social situation, or any other condition that would limit informed consent and/or compliance with trial requirements or may interfere with the interpretation of study results, as judged by Investigator or Sponsor.
* Has any clinically significant gastrointestinal conditions or abnormalities that may alter absorption or swallowing
* Known contraindication or hypersensitivity to momelotinib and its metabolites, or any of their excipients.
* Presence of peripheral neuropathy \>=Grade 2 per NCI CTCAE v6.0.
* Known history of disseminated mycobacterial infection.
* Known positive status for human immunodeficiency virus (HIV).
* Positive QuantiFERON (or other interferon gamma release assay) during Screening.
* Unable to receive any Pneumocystis jiroveci pneumonia (PJP) medical prophylaxis
* Known clinically significant anemia due to iron, vitamin B12 or folate deficiencies, or autoimmune or hereditary hemolytic anemia, gastrointestinal bleeding, or thalassemia.
* More than 1 prior line of VEXAS directed therapy before or after VEXAS diagnosis or other medical condition.
* Use of the following treatments within the noted time periods referenced from date of randomization:
1. VEXAS-directed therapies (washout period) up to 5 half-lives or up 14 days if half-life is \<3 days
2. Other non-GC anti-inflammatory therapies: for non-biologics): 14 days or five half-lives, whichever is longer; for biologics): 28 days or two half-lives whichever is longer.
3. Hematologic support therapy (e.g., ESAs, danazol, luspatercept, G-CSF): 4 weeks
4. Cell-depleting therapies such as anti-CD20 (rituximab): 12 months
5. Investigational agent from a class not otherwise specified: 5 half-lives or 60 days, whichever is longer
* GC use for conditions other than VEXAS, which would interfere with adherence to the fixed GC taper regimen and/or to assessment of efficacy.
* Chronic use of systemic corticosteroids for \>4 years or inability to withdraw corticosteroid treatment
* Planned allogeneic HSCT for MDS or VEXAS, within 1 year.
* Any major surgery within 28 days prior to randomization.
* Prior allogeneic/autologous stem cell transplant or solid organ transplant (other than corneal).
* Presence of peripheral neuropathy \>=Grade 2 per NCI CTCAE v6.0.
* Hepatitis B or C active infection, unless protocol defined criteria are met.
* Any of the following conditions within 6 months prior to randomization:
1. Unstable angina pectoris
2. Symptomatic congestive heart failure
3. Uncontrolled cardiac arrhythmia
4. QTc \>450 msec or QTc \>480 msec for participants with bundle branch block.
