In response to the energy crisis resulting from submergence stress and hypoxia, Arabidopsis limits non-essential mRNAs translation, and accumulate cytosolic stress granules (SG). SGs are phase-separated mRNA-protein particles that partition transcripts for various fates: storage, degradation, or return to translation after stress alleviation. Here, it is shown that RNA stress granules are dynamically regulated during hypoxia stress and aerobic recovery via two phases of autophagy that require the AAA+ ATPase CDC48 and the calcium sensor Calmodulin-like 38 (CML38). CML38 is a core hypoxia response-protein that associates with hypoxia-induced SGs. We show that CML38 is essential for SG autophagy during extended hypoxia. Further, cml38 mutants show disorganized SG morphology during extended hypoxia, suggesting a role in SG formation and maintenance. We also show that upon the return of aerobic conditions, intracellular calcium and CML38 are necessary for SG breakdown and turnover, and for upregulating autophagy. cml38 mutants not only lose these responses, but also have aberrant, sustained autophagosome accumulation during the reoxygenation recovery phase. The findings suggest that CDC48 RNA granule autophagy (“granulophagy”) is conserved in plants, and that the hypoxia-induced calcium sensor CML38 regulates SG autophagy during anaerobic stress as well as during the reprogramming phase associated with reoxygenation.