  We present radio observations of GRB 020405 starting 1.2 days after the
burst, which reveal a rapidly-fading ``radio flare''. Based on its temporal and
spectral properties, we interpret the radio flare as emission from the reverse
shock. This scenario rules out a circumburst medium with a radial density
profile \rho ~ r^{-2} expected around a mass-losing massive star, since in that
case the reverse shock emission decays on the timescale of the burst duration
t~100 s. Using published optical and X-ray data, along with the radio data
presented here, we further show that a self-consistent model requires
collimated ejecta with an opening angle of 6 degrees (t_j~0.95 days). As a
consequence of the early jet break, the late-time (t>10 days) emission measured
with the Hubble Space Telescope significantly deviates from an extrapolation of
the early, ground-based data. This, along with an unusually red spectrum, F_\nu
\~ \nu^{-3.9}, strengthens the case for a supernova that exploded at about the
same time as GRB 020405, thus pointing to a massive stellar progenitor for this
burst. This is the first clear association of a massive progenitor with a
uniform medium, indicating that a \rho ~ r^{-2} profile is not a required
signature, and in fact may not be present on the lengthscales probed by the
afterglow in the majority of bursts.
