The isospin asymmetries of B→K(∗)μ+μ− decays and the partial branching fractions of B0→K0μ+μ− and B+→K∗+μ+μ− are measured as a function of the di-muon mass squared q2 using an integrated luminosity of 1.0 fb−1 collected with the LHCb detector. The B→Kμ+μ− isospin asymmetry integrated over q2 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 B0→K0Sμ+μ− is reported with 5.7 σ significance. Assuming that the branching fraction of B0→K0μ+μ− is twice that of B0→K0Sμ+μ−, the branching fractions of B0→K0μ+μ− and B→K∗+μ+μ− are found to be (0.31+0.07−0.06)×10−6 and (1.16±0.19)×10−6, respectively.