  We report on a search for the flavor-changing neutral current decay
D^0\to\mu^+\mu^- in p\bar{p} collisions at \sqrt{s}=1.96 TeV using 65\ipb of
data collected by the CDF II experiment at the Fermilab Tevatron Collider. A
displaced-track trigger selects long-lived D^0 candidates in the
D^0\to\mu^+\mu^- search channel, the kinematically similar D^0\to\pi^+\pi^-
channel used for normalization, the Cabbibo-favored D^0\to K^+\pi^- channel
used to optimize the selection criteria in an unbiased manner, and their charge
conjugates. Finding no signal events in the D^0\to\mu^+\mu^- search window, we
set an upper limit on the branching fraction {\cal B}(D^0\to\mu^+\mu^-)\leq
2.5E-6 (3.3E-6) at the 90% (95%) confidence level.
