Intracellular pathogens cause membrane distortion and damage as they enter host cells. Cells perceive these membrane alterations as danger signals and respond by activating autophagy. This response has primarily been studied during bacterial invasion, and only rarely in viral infections. Here, we investigate the cellular response to membrane damage during adenoviral entry. Adenoviruses and their vector derivatives, that are an important vaccine platform against SARS-CoV-2, enter the host cell by endocytosis followed by lysis of the endosomal membrane. We previously showed that cells mount a locally confined autophagy response at the site of endosomal membrane lysis. Here we describe the mechanism of autophagy induction: endosomal membrane damage activates the kinase TBK1 that accumulates in its phosphorylated form at the penetration site. Activation and recruitment of TBK1 require detection of membrane damage by galectin 8 but occur independently of classical autophagy receptors or functional autophagy. Instead, TBK1 itself promotes subsequent autophagy that adenoviruses need to take control of. Depletion of TBK1 reduces LC3 lipidation during adenovirus infection and restores the infectivity of an adenovirus mutant that is restricted by autophagy. By comparing adenovirus-induced membrane damage to sterile lysosomal damage, we implicate TBK1 in the response to a broader range of types of membrane damage. Our study thus highlights an important role for TBK1 in the cellular response to adenoviral endosome penetration and places TBK1 early in the pathway leading to autophagy in response to membrane damage.