Studying how epithelia respond to mechanical stresses is key to understanding tissue shape changes during morphogenesis. Here, we study the viscoelastic properties of the Drosophila wing epithelium during pupal morphogenesis by quantifying mechanical stress and cell shape as a function of time. We find a delay of 8 h between maximal tissue stress and maximal cell elongation, indicating a viscoelastic deformation of the tissue. We show that this viscoelastic behavior emerges from the mechanosensitivity of endocytic E-cadherin turnover. The increase in E-cadherin turnover in response to stress is mediated by mechanosensitive relocalization of the E-cadherin binding protein p120-catenin (p120) from cell junctions to cytoplasm. Mechanosensitivity of E-cadherin turnover is lost in p120 mutant wings, where E-cadherin turnover is constitutively high. In this mutant, the relationship between mechanical stress and stress-dependent cell dynamics is altered. Cells in p120 mutant deform and undergo cell rearrangements oriented along the stress axis more rapidly in response to mechanical stress. These changes imply a lower viscosity of wing epithelium. Taken together, our findings reveal that p120-dependent mechanosensitive E-cadherin turnover regulates viscoelastic behavior of epithelial tissues. How epithelial junctional networks remodel in response to tissue stress is key to morphogenesis. Iyer et al. show that mechanical stress increases endocytic turnover of E-cadherin by depleting the E-cadherin binding protein p120 from cell junctions. This speeds remodeling of the junctional network and decreases cell shape viscosity.