The role of perceived experts (i.e., medical professionals and biomedical scientists) as potential anti-vaccine influencers has not been characterized systematically. We describe the prevalence and importance of anti-vaccine perceived experts by constructing a coengagement network based on a Twitter data set containing over 4.2 million posts from April 2021. The coengagement network primarily broke into two large communities that differed in their stance toward COVID-19 vaccines, and misinformation was predominantly shared by the anti-vaccine community. Perceived experts had a sizable presence within the anti-vaccine community and shared academic sources at higher rates compared to others in that community. Perceived experts occupied important network positions as central anti-vaccine nodes and bridges between the anti- and pro-vaccine communities. Perceived experts received significantly more engagements than other individuals within the anti- and pro-vaccine communities and there was no significant difference in the influence boost for perceived experts between the two communities. Interventions designed to reduce the impact of perceived experts who spread anti-vaccine misinformation may be warranted.