The safety of the tissue transplant recipient is a top priority for tissue banks, and the emergence of the new coronavirus SARS-CoV-2 has raised significant concerns about the risks of releasing tissue for clinical use. In the present study, we conducted a literature review about the potential infectivity of SARS-CoV-2 in different biological tissues and the influence of various tissue processing and sterilization procedures on viral inactivation. The search revealed that SARS-CoV-2 binds to the human angiotensin-converting enzyme receptor to penetrate human cells. These receptors are present in skin cells, musculoskeletal tissue, amniotic membranes, cardiovascular tissue and ocular tissues, including the cornea. In general, we found that coronaviruses are stable at low temperatures, and inactivated upon exposure to extreme heat and pH. Notably, gamma irradiation, which has already been employed to inactivate SARS and MERS, could be useful for sterilizing skin, amnion and musculoskeletal tissues against SARS-CoV-2. We conclude that due to the limited information about the effects of physical and chemical tissue processing methods on viral neutralization, rigorous donor screening is still essential for tissue transplant recipient safety.