A study of the decays B0s→μ+μ− and B0→μ+μ− has been performed using data corresponding to an integrated luminosity of 25 fb−1 of 7 and 8 TeV proton–proton collisions collected with the ATLAS detector during the LHC Run 1. For the B0 dimuon decay, an upper limit on the branching fraction is set at B(B0→μ+μ−) < 4.2×10−10 at 95 % confidence level. For B0s, the branching fraction B(B0s→μ+μ−) = (0.9+1.1−0.8) × 10−9 is measured. The results are consistent with the Standard Model expectation with a p value of 4.8 %, corresponding to 2.0 standard deviations.