Study to Evaluate the Pharmacokinetics, Pharmacodynamics, Safety, and Tolerability of Inebilizumab in Pediatric Participants With IgG4-RD

Key Inclusion Criteria: 1. Participants must weigh ≥ 17 kg to be eligible for enrollment. 2. Participant has provided informed consent/assent before initiation of any study-specific activities/procedures. Participant's legally authorized representative has provided informed consent when the participant is legally too young to provide informed consent, and the participant has provided written assent based on local regulations and/or guidelines before any study-specific activities/procedures being initiated. 3. Age 2 to \< 18 years at the time of screening. For participants who reach the age of legal consent during the clinical study, notification will be required, and a new consent form must be signed by the participant for continuation in the study. 4. Clinical diagnosis of IgG4-RD. 5. Fulfillment of the 2019 American College of Rheumatology (ACR) and the European League Against Rheumatism (EULAR) classification criteria as determined by the principal investigator (PI) at screening. Specifically, participants must meet the classification criteria entry requirements (including involvement of one of the following organs: pancreas, bile ducts/biliary tree, orbits, lungs, kidneys, lacrimal glands, major salivary glands, retroperitoneum, aorta, pachymeninges, or thyroid gland \[Riedel's thyroiditis\]), must not meet any of the classification criteria exclusions, and must achieve at least 20 classification criteria inclusion points. 6. Receipt of all age-appropriate and locally-required vaccinations before screening. 7. Participants requiring treatment in addition to or other than glucocorticoids (GCs) for IgG4-RD according to PI's assessment at screening. 8. Participants who are on GCs for the treatment of IgG4-RD should remain on a stable dose for at least 2 weeks before enrollment (Day 1). Tapering post enrollment will be at PI's discretion. Key Exclusion Criteria: 1. Participants with any of the following abnormal liver function tests in the presence of hepatobiliary IgG4-RD activity: * aspartate aminotransferase (AST) \> 10 × upper limit of normal (ULN) * alanine aminotransferase (ALT) \> 10 × ULN * total bilirubin (TBL) \> 5 × ULN Screening liver function tests may be repeated before Day 1 to permit abnormal values due to hepatobiliary IgG4-RD activity to respond to GC treatment. 2. Evidence of significant hepatic, renal, or metabolic dysfunction or significant hematological abnormality, including any of the following at screening (one repeat test may be conducted to confirm results within the same screening period): * platelet count \< 75000/μL (or \< 75 × 109/L) * absolute neutrophil count \< 1200 cells/μL * total Ig \< 600 mg/dL * CD4 T lymphocyte count \< 300 cells/µL * hemoglobin \< 8 g/dL (or \< 80 g/L). 3. Estimated glomerular filtration rate \< 45 mL/min/1.73 m\^2. 4. B-cell counts \< one-half of the lower limit of normal (LLN) for age according to the central laboratory. 5. Diagnosed with a concurrent autoimmune disease that is uncontrolled or requires any prohibited medication (unless approved by the medical monitor). 6. Clinically significant serious active or chronic viral, bacterial, or fungal infection that requires treatment with anti-infectives, hospitalization, or, in the investigator's opinion, represents an additional risk to the participant, within 2 months before Day 1 of study. 7. Known history of congenital or acquired immunodeficiency (eg, due to human immunodeficiency virus \[HIV\] infection, splenectomy, immunosuppression-related or idiopathic T-cell deficiencies) that predisposes the participant to infection. 8. Positive test for chronic hepatitis B infection at screening, defined as either: (1) Positive hepatitis B surface antigen (HBsAg); or (2) Positive hepatitis B core antibody (anti-HBc) PLUS negative hepatitis B surface antibody (anti-HBs). Note: Participants with a positive anti-HBs only, or a positive anti-HBc plus positive anti-HBs and negative HBsAg, are eligible to enroll. 9. Receipt of any of the following before Day 1: alemtuzumab, total lymphoid irradiation, bone marrow transplant, T-cell vaccination therapy. 10. Receipt of any of the following within 2 months before Day 1: azathioprine, mycophenolate mofetil, cyclosporine, methotrexate, cyclophosphamide, tocilizumab, satralizumab, eculizumab, and mitoxantrone. 11. Receipt of rituximab or any experimental B-cell depleting agent (eg, ocrelizumab, obinutuzumab, ofatumumab, inebilizumab), or any non-depleting B-cell-directed therapy (eg, belimumab), abatacept, within 6 months before screening unless B-cell counts have returned to ≥ one-half the LLN. 12. Receipt of any live or attenuated vaccine (administration of inactivated \[killed\] vaccine is acceptable) within 4 weeks before Day 1, Bacillus Calmette-Guérin vaccine within 1 year of screening, or blood transfusion within 4 weeks before screening or during screening.