African swine fever virus (ASFV) is a large, enveloped DNA virus that assembles in perinuclear sites located close to the centrosome. It is reported here that the microtubule network becomes disorganized soon after the onset of viral DNA replication and formation of assembly sites. ASFV infection resulted in loss of γ-tubulin and pericentrin at the centrosome; this was due to protein relocalization, but not degradation. ASFV infection also inhibited the ability of the centrosome to nucleate microtubules. The reorganization of microtubules seen in ASFV-infected cells may therefore be mediated by γ-tubulin and pericentrin redistribution, and consequent disruption of centrosome assembly and function.