  The LHCb has measured the ratios of $B\to K^\ast\mu^+\mu^-$ to $B\to K^\ast
e^+ e^-$ branching fractions in two dilepton invariant mass squared bins, which
deviate from the Standard Model predictions by approximately $2.5\sigma$. These
new measurements strengthen the hint of lepton flavor universality breaking
which was observed earlier in $B\to K\ell^+\ell^-$ decays. In this work we
explore the possibility of explaining these anomalies within the framework of
$R$-parity violating interactions. In this framework, $b\to s\ell^+\ell^-$
transitions are generated through tree and one loop diagrams involving exchange
of down-type right-handed squarks, up-type left-handed squarks and left-handed
sneutrinos. We find that the tree level contributions are not enough to explain
the anomalies, but at one loop, simultaneous explanation of the deviations in
$B\to K^\ast\ell^+\ell^-$ and $B\to K\ell^+\ell^-$ is feasible for a parameter
space of the Yukawa couplings that is consistent with the bounds coming from
$B\to K^{(\ast)}\nu\bar{\nu}$ and $D^0\to \mu^+\mu^-$ decays and
$B_s-\bar{B}_s$ mixing.
