Inclusion Criteria:  Hospitalized with coronavirus (SARS-CoV-2) infection. Male or female participants from 1 to <18 years of age. Requires supplemental oxygen and have chest imaging findings to confirm respiratory disease due to COVID-19 within 72 hours of study entry and enrollment. Supplemental oxygen including but not limited to: nasal cannula, mask, high flow devices, CPAP/BiPAP, invasive mechanical ventilation as well as ECMO.  Exclusion Criteria:  Are receiving biologic treatments (such as Tumor Necrosis Factor [TNF] inhibitors, interleukin inhibitors, T-cell or B-cell targeted therapies, interferon, or Janus kinase (JAK) inhibitors); or are receiving other immunosuppressants such that, in the opinion of the investigator, participating in the study would put the participant at an unacceptable risk of immunosuppression.  Note: A washout period is required prior to screening.  Are receiving strong inhibitors of Organic Anion Transporter 3 (OAT3) (such as probenecid) that cannot be discontinued at study entry. Have diagnosis of current active tuberculosis (TB) or, if known, latent TB treated for less than 4 weeks with appropriate anti-tuberculosis therapy per local guidelines (by history only, no screening tests required). Suspected serious, active bacterial, fungal, viral, or other infection (besides COVID-19) that in the opinion of the investigator could constitute a risk when taking investigational product. Have received any live vaccine within 4 weeks before screening, or intend to receive a live vaccine during the study. Note: Use of non-live (inactivated) vaccinations are allowed for all participants. Require invasive mechanical ventilation, including extracorporeal membrane oxygenation (ECMO) at study entry. Current diagnosis of active malignancy that, in the opinion of the investigator, could constitute a risk when taking investigational product. Have a history of venous thromboembolism (VTE) (deep vein thrombosis [DVT] and/or pulmonary embolism [PE]) or considered high risk of VTE (DVT/PE). Anticipated discharge from the hospital, or transfer to another hospital (or another unit), which is not a study site within 72 hours after study entry. Have neutropenia (absolute neutrophil count <1000 cells/microliters). Have lymphopenia (absolute lymphocyte count <200 cells/microliters). Have alanine aminotransferase (ALT) or aspartate aminotransferase (AST) >5 times AAULN. Estimated glomerular filtration rate (eGFR) (Modification of Diet in Renal Disease [MDRD]) <40 milliliter/minute/1.73 meters squared. Have a known hypersensitivity to baricitinib or any of its excipients. Are currently enrolled in any other clinical study involving an investigation product or any other type of medical research judged not to be scientifically or medically compatible with this study. Note: The participant should not be enrolled (started) in another clinical trial for the treatment of COVID-19 or SARS CoV-2 through Day 28. Are pregnant, or intend to become pregnant or breastfeed during the study. Are, in the opinion of the investigator or sponsor, at risk of immunosuppression or otherwise unsuitable for inclusion in the study. Are using or will use extracorporeal blood purification (EBP) device to remove proinflammatory cytokines from the blood such as a cytokine absorption or filtering device, for example, CytoSorb®. Are, in the opinion of the investigator, unlikely to survive for at least 48 hours after screening.