We report on a search for B0s→μ+μ− and B0→μ+μ− decays using proton-antiproton collision data at s√=1.96 TeV corresponding to 10 fb−1 of integrated luminosity collected by the CDF II detector at the Fermilab Tevatron collider. The observed number of B0 candidates is consistent with background-only expectations and yields an upper limit on the branching fraction of B(B0→μ+μ−)<4.6×10−9 at 95% confidence level. We observe an excess of B0s candidates. The probability that the background processes alone could produce such an excess or larger is 0.94%. The probability that the combination of background and the expected standard model rate of B0s→μ+μ− could produce such an excess or larger is 6.8%. These data are used to determine a branching fraction B(B0s→μ+μ−)=(1.3+0.9−0.7)×10−8 and provide an upper limit of B(B0s→μ+μ−)<3.1×10−8 at 95% confidence level.