  A high energy muon collider can provide new and complementary discovery
potential to the LHC or future hadron colliders. Leptoquarks are a motivated
class of exotic new physics models, with distinct production channels at hadron
and lepton machines. We study a vector leptoquark model at a muon collider with
$\sqrt{s} = 3, 14$ TeV within a set of both UV and phenomenologically motivated
flavor scenarios. We compute which production mechanism has the greatest reach
for various values of the leptoquark mass and the coupling between leptoquark
and Standard Model fermions. We find that we can probe leptoquark masses up to
an order of magnitude beyond $\sqrt{s}$ with perturbative couplings.
Additionally, we can also probe regions of parameter space unavailable to
flavor experiments. In particular, all of the parameter space of interest to
explain recent low-energy anomalies in B meson decays would be covered even by
a $\sqrt{s} = 3$ TeV collider.
