Superconducting diodes that support nonreciprocal supercurrent flow in principle constitute attractive, nondissipative, circuit elements for superconducting electronics. But their realization faces fundamental challenges, as conventional Josephson tunnel junctions are inherently reciprocal. The so far existing approaches to break the reciprocity typically involve magnetism or spin-orbit coupling, which often increase the device complexity and limit the reproducibility. Here, we demonstrate an alternative dynamical route to supercurrent nonreciprocity based on parametric driving. By applying a frequency-modulated supercurrent amplitude, we show that effective higher-order, nonharmonic terms are generated in the current-phase relation. Leveraging strong mathematical similarities with the Kapitza pendulum, we show that these terms dynamically break the reciprocity. This establishes the concept of a Kapitza supercurrent diode and demonstrates that nonreciprocal superconducting transport can be engineered by a nonequilibrium driving the conventional Josephson tunnel junctions. We propose two implementations of such a Kapitza supercurrent diode—via gate-controlled superconducting interferometers or flux-driven double-loop SQUIDs—to achieve nonreciprocal supercurrent transport within experimentally accessible frequencies ω / 2 π ∼ 1 to 10 GHz.