Electrical impulse generation and its conduction within cells or cellular networks are the cornerstone of electrophysiology. However, the advancement of the field is limited by sensing accuracy and the scalability of current recording technologies. Here we describe a scalable platform that enables accurate recording of transmembrane potentials in electrogenic cells. The platform employs a three-dimensional high-performance field-effect transistor array for minimally invasive cellular interfacing that produces faithful recordings, as validated by the gold standard patch clamp. Leveraging the high spatial and temporal resolutions of the field-effect transistors, we measured the intracellular signal conduction velocity of a cardiomyocyte to be 0.182 m s^-1, which is about five times the intercellular velocity. We also demonstrate intracellular recordings in cardiac muscle tissue constructs and reveal the signal conduction paths. This platform could provide new capabilities in probing the electrical behaviours of single cells and cellular networks, which carries broad implications for understanding cellular physiology, pathology and cell-cell interactions.