  The isospin asymmetries of $B \to K^{(*)}\mu^+\mu^-$ decays and the partial
branching fractions of $B^0 \to K^0\mu^+\mu^-$ and $B^+ \to K^{*+}\mu^+\mu^-$
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 $B
\to K\mu^+\mu^-$ isospin asymmetry integrated over $q^2$ is negative, deviating
from zero with over 4 $\sigma$ significance. The $B \to K^{*}\mu^+\mu^-$ decay
measurements are consistent with the Standard Model prediction of negligible
isospin asymmetry. The observation of the decay $B^0 \to
K^0_{\rm\scriptscriptstyle S}\mu^+\mu^-$ is reported with 5.7 $\sigma$
significance. Assuming that the branching fraction of $B^0 \to K^0\mu^+\mu^-$
is twice that of $B^0 \to K^0_{\rm\scriptscriptstyle S}\mu^+\mu^-$, the
branching fractions of $B^0 \to K^0\mu^+\mu^-$ and $B \to K^{*+}\mu^+\mu^-$ are
found to be ($0.31^{+0.07}_{-0.06}) \times 10^{-6}$ and ($1.16\pm0.19) \times
10^{-6}$, respectively.
