Velocity interferometers are typically used to measure velocities of surfaces at a single point or along an imaged line as a function of time. We describe an optical arrangement that enables high-resolution measurements of the two-dimensional velocity field across a shock front or shocked interface. The technique is employed to measure microscopic fluctuations in shock fronts that have passed through materials being considered as ablators for indirect-drive inertial confinement fusion. With picosecond time resolution the instrument captures velocity modes with wavelengths as short as 2.5 microm at a resolution of approximately 10 m/s rms on velocity fields averaging many km/s over an 800 microm field of view.