  We report on a search for the flavor-changing neutral current decays B^+ ->
mu^+ mu^- K^+ and B^0 -> mu^+ mu^- K^{*0} using 88 pb^{-1} of data from p-pbar
collisions at \sqrt{s}=1.8 TeV, collected with the Collider Detector at
Fermilab. Finding no evidence for these decays, we set upper limits on the
branching fractions B(B^+ -> mu^+ mu^- K^+) < 5.2x10^{-6} and B(B^0 -> mu^+
mu^-K^{*0}) < 4.0x10^{-6} at the 90% confidence level.
