Proteostasis is important for protecting cells from harmful proteins and is mainly controlled by the HSF1 (heat shock transcription factor 1) stress response pathway. This pathway facilitates protein refolding by molecular chaperones; however, it is unclear whether it functions in autophagy or inclusion formation. The autophagy receptor SQSTM1/p62 is involved in selective autophagic clearance and inclusion formation by harmful proteins, and its phosphorylation at S349, S403, and S407 is required for binding to substrates. Here, we demonstrate that casein kinase 1 phosphorylates the SQSTM1 S349 residue when harmful proteins accumulate. Investigation of upstream factors showed that both SQSTM1 S349 and SQSTM1 S403 residues were phosphorylated in an HSF1 dependent manner. Inhibition of SQSTM1 phosphorylation suppressed inclusion formation by ubiquitinated proteins and prevented colocalization of SQSTM1 with aggregation-prone proteins. Moreover, HSF1 inhibition impaired aggregate-induced autophagosome formation and elimination of protein aggregates. Our findings indicate that HSF1 triggers SQSTM1-mediated proteostasis.