The ongoing pandemic COVID-19, caused by SARS-CoV-2, has already resulted in more than 3 million cases and more than 200,000 deaths globally. Significant clinical presentations of COVID-19 include respiratory symptoms and pneumonia. In a minority of patients, extrapulmonary organs (central nervous system, eyes, heart, and gut) are affected, with detection of viral RNA in bodily secretions (stool, tears, and saliva). Infection of such extrapulmonary organs may serve as a reservoir for SARS-CoV-2, representing a potential source of viral shedding after the cessation of respiratory symptoms in recovered patients or in asymptomatic individuals. It is extremely important to understand this phenomenon, as individuals with intermittent virus shedding could be falsely identified as reinfected and may benefit from ongoing antiviral treatment. The potential of SARS-CoV-2 infection to rapidly disseminate and infect extrapulmonary organs is likely mediated through the nonstructural and accessory proteins of SARS-CoV-2, which act as ligands for host cells, and through evasion of host immune responses. The focus of this perspective is the extrapulmonary tissues affected by SARS-CoV-2 and the potential implications of their involvement for disease pathogenesis and the development of medical countermeasures.