Human tripartite motif protein 5α (TRIM5α) is a well-characterized restriction factor for some RNA viruses, including HIV1–5; however, reports are limited for DNA viruses6,7. Here we demonstrate that TRIM5α also restricts orthopoxviruses and, via its SPRY domain, binds to the orthopoxvirus capsid protein L3 to diminish virus replication and activate innate immunity. In response, several orthopoxviruses, including vaccinia, rabbitpox, cowpox, monkeypox, camelpox and variola viruses, deploy countermeasures. First, the protein C6 binds to TRIM5 via the RING domain to induce its proteasome-dependent degradation. Second, cyclophilin A (CypA) is recruited via interaction with the capsid protein L3 to virus factories and virions to antagonize TRIM5α; this interaction is prevented by cyclosporine A (CsA) and the non-immunosuppressive derivatives alisporivir and NIM811. Both the proviral effect of CypA and the antiviral effect of CsA are dependent on TRIM5α. CsA, alisporivir and NIM811 have antiviral activity against orthopoxviruses, and because these drugs target a cellular protein, CypA, the emergence of viral drug resistance is difficult. These results warrant testing of CsA derivatives against orthopoxviruses, including monkeypox and variola.