Targeted protein degradation plays important roles in stress responses in all cells. In E. coli, the membrane-bound AAA+ FtsH protease degrades cytoplasmic and membrane proteins. Here, we demonstrate that FtsH degrades cyclopropane fatty acid (CFA) synthase, whose synthesis is induced upon nutrient deprivation and entry into stationary phase. We find that neither the disordered N-terminal residues nor the structured C-terminal residues of the kinetically stable CFA-synthase dimer are required for FtsH recognition and degradation. Experiments with fusion proteins support a model in which an internal degron mediates FtsH recognition as a prelude to unfolding and proteolysis. These findings elucidate the terminal step in the life cycle of CFA synthase and provide new insight into FtsH function.