The isospin asymmetries of B → K (*)μ +μ - decays and the partial branching fractions of B 0 → K 0μ +μ - and B +→ K *+μ +μ - are measured as a function of the di-muon mass squared q 2 using an integrated luminosity of 1.0fb -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 s0μ +μ - is reported with 5.7 σ significance. Assuming that the branching fraction of B 0 → K 0μ +μ - is twice that of B 0 → K s0μ +μ -, the branching fractions of B 0 → K 0μ +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.