The coronavirus disease 19 (COVID-19) pandemic is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), a coronavirus that spilled over from the bat reservoir. Despite numerous clinical trials and vaccines, the burden remains immense, and the host determinants of SARS-CoV-2 susceptibility and COVID-19 severity remain largely unknown. Signatures of positive selection detected by comparative functional genetic analyses in primate and bat genomes can uncover important and specific adaptations that occurred at virus–host interfaces. We performed high-throughput evolutionary analyses of 334 SARS-CoV-2-interacting proteins to identify SARS-CoV adaptive loci and uncover functional differences between modern humans, primates, and bats. Using DGINN (Detection of Genetic INNovation), we identified 38 bat and 81 primate proteins with marks of positive selection. Seventeen genes, including the ACE2 receptor, present adaptive marks in both mammalian orders, suggesting common virus–host interfaces and past epidemics of coronaviruses shaping their genomes. Yet, 84 genes presented distinct adaptations in bats and primates. Notably, residues involved in ubiquitination and phosphorylation of the inflammatory RIPK1 have rapidly evolved in bats but not primates, suggesting different inflammation regulation versus humans. Furthermore, we discovered residues with typical virus–host arms race marks in primates, such as in the entry factor TMPRSS2 or the autophagy adaptor FYCO1, pointing to host-specific in vivo interfaces that may be drug targets. Finally, we found that FYCO1 sites under adaptation in primates are those associated with severe COVID-19, supporting their importance in pathogenesis and replication. Overall, we identified adaptations involved in SARS-CoV-2 infection in bats and primates, enlightening modern genetic determinants of virus susceptibility and severity.