We present a novel polarization-based spectroscopic method developed for measuring the radial component of the magnetic field, Br, in an imploding magnetized-plasma column. The method is based on the combined effects of the Zeeman splitting and the Doppler shift. In the experiment, we use imploding oxygen plasma with a pre-embedded axial magnetic field Bz. Due to the axial non-uniformity of the plasma implosion and the field compression, the Bz lines are bent radially. We measure the magnitude and direction of B⃗ along the radial coordinate; the magnitude is found to constitute a substantial fraction of the total B⃗ in the compressed plasma. The measurements extend the capabilities of spectroscopic diagnostics in magnetized plasmas, enabling a deeper understanding of the plasma dynamics (such as plasma rotation) and the energy flow in plasmas under high-current pulses.