  A search is presented for dark matter in proton-proton collisions at a
center-of-mass energy of $\sqrt{s} =$ 13 TeV using events with at least one
high transverse momentum ($p_\mathrm{T}$) muon, at least one
high-$p_\mathrm{T}$ jet, and large missing transverse momentum. The data were
collected with the CMS detector at the CERN LHC in 2016 and 2017, and
correspond to an integrated luminosity of 77.4 fb$^{-1}$. In the examined
scenario, a pair of scalar leptoquarks is assumed to be produced. One
leptoquark decays to a muon and a jet while the other decays to dark matter and
low-$p_\mathrm{T}$ standard model particles. The signature for signal events
would be significant missing transverse momentum from the dark matter in
conjunction with a peak at the leptoquark mass in the invariant mass
distribution of the highest $p_\mathrm{T}$ muon and jet. The data are observed
to be consistent with the background predicted by the standard model. For the
first benchmark scenario considered, dark matter masses up to 500 GeV are
excluded for leptoquark masses $M_\mathrm{LQ}$ $\approx$ 1400 GeV, and up to
300 GeV for $M_\mathrm{LQ}$ $\approx$ 1500 GeV. For the second benchmark
scenario, dark matter masses up to 600 GeV are excluded for $M_\mathrm{LQ}$
$\approx$ 1400 GeV.
