Biohybrid systems have been developed to better understand the design principles and coordination mechanisms of biological systems. We consider whether two functional regulatory features of the heart-mechanoelectrical signaling and automaticity-could be transferred to a synthetic analog of another fluid transport system: a swimming fish. By leveraging cardiac mechanoelectrical signaling, we recreated reciprocal contraction and relaxation in a muscular bilayer construct where each contraction occurs automatically as a response to the stretching of an antagonistic muscle pair. Further, to entrain this closed-loop actuation cycle, we engineered an electrically autonomous pacing node, which enhanced spontaneous contraction. The biohybrid fish equipped with intrinsic control strategies demonstrated self-sustained body-caudal fin swimming, highlighting the role of feedback mechanisms in muscular pumps such as the heart and muscles.