The isospin asymmetries of B → K (∗) μ + μ − decays and the partial branching fractions of B 0 → K 0 μ + μ − and B + → K ∗+ μ + μ − are measured as a function of the di-muon mass squared q 2 using an integrated luminosity of 1.0 fb−1 collected with the LHCb detector. The B → Kμ + μ − isospin asymmetry integrated over q 2 is negative, deviating from zero with over 4 σ significance. The B → K ∗ μ + μ − decay measurements are consistent with the Standard Model prediction of negligible isospin asymmetry. The observation of the decay B 0 → K S μ + μ − is reported with 5.7 σ significance. Assuming that the branching fraction of B 0 → K 0 μ + μ − is twice that of B 0 → K S μ + μ −, the branching fractions of B 0 → K 0 μ + μ − and B → K ∗+ μ + μ − are found to be (0.31−0.06) × 10−6 and (1.16 ± 0.19) × 10−6, respectively.