It has been a long time since the world has experienced a pandemic with such a rapid devastating impact as the current COVID-19 pandemic. The causative agent, the Severe Acute Respiratory Syndrome coronavirus 2 (SARS-CoV-2) is further unusual in that it appears capable of infecting many different mammal species. As a significant proportion of people worldwide are infected with SARS-CoV-2 and may spread the infection unknowingly before symptoms occur or without any symptoms ever occurring, there is a non-negligible risk of humans spreading SARS-CoV-2 to wildlife, in particular mammals. Because of SARS-CoV-2’s evolutionary origins in bats and reports of humans transmitting the virus to pets and zoo animals, regulations for prevention of human-to-animal transmission have so far focused mostly on these animal groups. Here, we summarize recent studies and reports that show that a wide range of distantly related mammals are likely susceptible to SARS-CoV-2 and that susceptibility or resistance to the virus is in general not predictable, or only to some extent, by phylogenetic proximity to known susceptible or resistant hosts. In the absence of solid evidence on the SARS-CoV-2 susceptibility/resistance for each of the >5,500 mammal species, we argue that sanitary precautions should be taken when interacting with any mammal species in the wild. Preventing human-to-wildlife SARS-CoV-2 transmission is important for protecting these (sometimes endangered) animals from disease, but also to avoid establishment of novel SARS-CoV-2 reservoirs in wild animals. The risk of repeated re-infection of humans from such a wildlife reservoir could severely hamper SARS-CoV-2 control efforts. For wildlife fieldworkers interacting directly or indirectly with mammals, we recommend sanitary precautions such as physical distancing, wearing face masks and gloves, and frequent decontamination, which are very similar to regulations currently imposed to prevent transmission among humans.