Autophagy is an evolutionarily conserved degradation pathway in eukaryotes; it plays a critical role in nutritional stress tolerance. The circadian clock is an endogenous timekeeping system that generates biological rhythms to adapt to daily changes in the environment. Accumulating evidence indicates that the circadian clock and autophagy are intimately interwoven in animals. However, the role of the circadian clock in regulating autophagy has been poorly elucidated in plants. Here, we show that autophagy exhibits a robust circadian rhythm in both light/dark cycle (LD) and in constant light (LL) in Arabidopsis. However, autophagy rhythm showed a different pattern with a phase‐advance shift and a lower amplitude in LL compared to LD. Moreover, mutation of the transcription factor LUX ARRHYTHMO (LUX) removed autophagy rhythm in LL and led to an enhanced amplitude in LD. LUX represses expression of the core autophagy genes ATG2, ATG8a, and ATG11 by directly binding to their promoters. Phenotypic analysis revealed that LUX is responsible for improved resistance of plants to carbon starvation, which is dependent on moderate autophagy activity. Comprehensive transcriptomic analysis revealed that the autophagy rhythm is ubiquitous in plants. Taken together, our findings demonstrate that the LUX‐mediated circadian clock regulates plant autophagy rhythms.