The persistent hints of LFU violation in $b \to s \ell \ell$ may imply an existence of leptoquarks close to the TeV scale that couple to $b \mu$ and $s \mu$. These leptoquark Yukawa couplings can in full generality be complex and thus provide a new source of CP violation. We show that a large CP phase with a definite sign is perfectly viable for an $S_3$ leptoquark of mass below a few TeV, consistent with CP even and CP odd $b \to s \ell \ell$ and $B_s$ mixing observables. Furthermore, we show how the direct CP asymmetries in $B\to K \mu \mu$ are significantly enhanced in the vicinity of narrow charmonia, and that their measurement in the future could provide important additional information in constraining the potentially CP violating NP in $b \to s \ell \ell$.