  We study the penguin induced transition $b\to s\ \gamma$ in the minimal N=1
supersymmetric extension of the Standard Model with radiative breaking of the
electroweak group. We include the effects of one-loop corrections to the Higgs
potential and scalar masses. We show that the present upper and lower
experimental limits on the inclusive decay sharply constrain the parameter
space of the model in a wide range of $\tan\beta$ values. The implications of
the recently advocated relation $|B|\ge 2$ for the bilinear SUSY soft breaking
parameter in grand unified theories are also analyzed.
