Magnetic reconnection, the process whereby magnetic field lines break and then reconnect to form a different topology, underlies critical dynamics of magnetically confined plasmas in both nature(1-4) and the laboratory(5-9). Magnetic reconnection involves localized diffusion of the magnetic field across plasma, yet observed reconnection rates are typically much higher than can be accounted for using classical electrical resistivity(10). It is generally proposed(10) that the field diffusion underlying fast reconnection results instead from some combination of non-magnetohydrodynamic processes that become important on the 'microscopic' scale of the ion Larmor radius or the ion skin depth. A recent laboratory experiment(11) demonstrated a transition from slow to fast magnetic reconnection when a current channel narrowed to a microscopic scale, but did not address how a macroscopic magnetohydrodynamic system accesses the microscale. Recent theoretical models(12) and numerical simulations(13,14) suggest that a macroscopic, two-dimensional magnetohydrodynamic current sheet might do this through a sequence of repetitive tearing and thinning into two-dimensional magnetized plasma structures having successively finer scales. Here we report observations demonstrating a cascade of instabilities from a distinct, macroscopic-scale magnetohydrodynamic instability to a distinct, microscopic-scale (ion skin depth) instability associated with fast magnetic reconnection. These observations resolve the full three-dimensional dynamics and give insight into the frequently impulsive nature of reconnection in space and laboratory plasmas.