A Study of Ustekinumab in Participants With Active Polymyositis and Dermatomyositis Who Have Not Adequately Responded to One or More Standard-of-care Treatments

Inclusion Criteria: * Has a diagnosis of polymyositis (PM)/ dermatomyositis (DM) made or confirmed by a physician (such as a rheumatologist, neurologist, or dermatologist) experienced in treatment of PM/DM at least 6 weeks prior to first dose of the study drug * Has PM or DM which is considered active despite receiving at least 1 standard-of-care treatment by the investigator * Must be receiving 1 or more of the following protocol-permitted, systemic standard-of-care treatments: i) glucocorticoids, ii) 1 or 2 of the following immunomodulatory drugs: mycophenolate mofetil, azathioprine, oral methotrexate, oral tacrolimus, or oral cyclosporine A * Regular or as needed treatment with topical use of glucocorticoids are permitted to treat skin lesions on a stable dose for greater than or equal to (\>=) 2 weeks prior to first dose of the study drug * Contraceptive (birth control) use by men or women should be consistent with local regulations regarding the acceptable methods of contraception for those participating in clinical studies * Must be medically stable on the basis of clinical laboratory tests performed at screening. If the results of the clinical laboratory tests are outside the normal reference ranges, the participant may be included only if the investigator judges the abnormalities or deviations from normal to be not clinically significant * Demonstrable muscle weakness at screening and Week 0 measured by the Manual Muscle Testing (MMT)-8 less than or equal to (\<=)135 units * Demonstrable muscle weakness at screening measured by any 2 or more of the followings: (i) PhGA greater than or equal to (\>=) 1.5 centimeter (cm), (ii) 1 or more muscle enzymes (Creatine kinase \[CK\], and aldolase) \>=1.4\*upper limit of normal (ULN), (iii) Myositis disease activity assessment tool (MDAAT)-Extramuscular Global Assessment \>=1.5 cm Exclusion Criteria: * Has myositis other than PM/DM, including but not limited to amyopathic dermatomyositis (ADM), clinically amyopathic DM, juvenile DM, inclusion body myositis (IBM) immune-mediated necrotizing myopathy diagnosed based on muscle biopsy findings and positive anti-SRP or anti-HMGCR antibody, drug-induced myositis, PM associated with human immunodeficiency virus (HIV), and muscular dystrophy, congenital myopathy, metabolic myopathy, and mitochondrial myopathy * Has other inflammatory diseases that might confound the evaluations of efficacy, including but not limited to rheumatoid arthritis (RA), psoriatic arthritis (PsA), systemic lupus erythematosus (SLE), psoriasis, or Crohn's disease * Has severe respiratory muscle weakness confirmed by the investigator based on the consultation with a pulmonologist and the measures of respiratory muscle strength such as maximal inspiratory pressure (MIP) and maximal expiratory pressure (MEP) and/or maximal voluntary ventilation (MVV) measurements and lung capacity such as forced vital capacity (FVC). The results need to be within population appropriate normal limits * Has severe muscle damage (Myositis Damage Index-VAS \[Muscle Damage\] greater than (\>) 7 centimeter \[cm\]), permanent weakness due to a non-IIM cause, or myositis with cardiac dysfunction * Has glucocorticoid-induced myopathy which the investigator considers the primary cause of muscle weakness * Has positive test result of anti-melanoma differentiation-associated protein 5 (MDA5) antibody (anti clinically amyopathic dermatomyositis (C-ADM)-140 antibody). * Has had a nontuberculous mycobacterial infection or opportunistic infection * Has a history of, or ongoing, chronic or recurrent infectious disease * Has past history of severe Interstitial lung disease (ILD) flare, severe non-infectious lung inflammation which required active intervention, or multiple relapses of these conditions * Presence or history of malignancy within 5 years before screening