Tripartite motif (TRIM) proteins mediate antiviral host defences by either directly targeting viral components or modulating innate immune responses. Here we identify a mechanism of antiviral restriction in which a TRIM E3 ligase controls viral replication by regulating the structure of host cell centrosomes and thereby nuclear lamina integrity. Through RNAi screening we identified several TRIM proteins, including TRIM43, that control the reactivation of Kaposi's sarcoma-associated herpesvirus. TRIM43 was distinguished by its ability to restrict a broad range of herpesviruses and its profound upregulation during herpesvirus infection as part of a germline-specific transcriptional program mediated by the transcription factor DUX4. TRIM43 ubiquitinates the centrosomal protein pericentrin, thereby targeting it for proteasomal degradation, which subsequently leads to alterations of the nuclear lamina that repress active viral chromatin states. Our study identifies a role of the TRIM43-pericentrin-lamin axis in intrinsic immunity, which may be targeted for therapeutic intervention against herpesviral infections.