The imploding plasma column of a gas-puff Z pinch was used to compress an embedded axial magnetic field. Field compression ratios up to 180 times and peak compressed fields up to 1.6 MG were measured by Faraday rotation. Field compression by this method has the advantage of high repetition rate for applications in the controlled production of high-energy densities, solid-state studies, generation of short-wavelength radiation, reducing the ignition threshold for fusion, and particle acceleration.