We report on a search for the flavor-changing neutral-current decay D0→μ+μ− in pp¯ collisions at s√=1.96  TeV using 360  pb−1 of integrated luminosity collected by the CDF II detector at the Fermilab Tevatron collider. A displaced vertex trigger selects long-lived D0 candidates in the μ+μ−, π+π−, and K−π+ decay modes. We use the Cabibbo-favored D0→K−π+ channel to optimize the selection criteria in an unbiased manner, and the kinematically similar D0→π+π− channel for normalization. We set an upper limit on the branching fraction B(D0→μ+μ−)<2.1×10−7(3.0×10−7) at the 90% (95%) confidence level.