The Golgi complex is essential for the processing, sorting, and trafficking of newly synthesized proteins and lipids. Golgi turnover is regulated to meet different cellular physiological demands. The role of autophagy in the turnover of Golgi, however, has not been clarified. Here we show that CALCOCO1 binds the Golgi-resident palmitoyltransferase ZDHHC17 to facilitate Golgi degradation by autophagy during starvation. Depletion of CALCOCO1 in cells causes expansion of the Golgi and accumulation of its structural and membrane proteins. ZDHHC17 itself is degraded by autophagy together with other Golgi membrane proteins such as TMEM165. Taken together, our data suggest a model in which CALCOCO1 mediates selective Golgiphagy to control Golgi size and morphology in eukaryotic cells via its interaction with ZDHHC17.