  We explore the prospect of constraining light mediators at the next
generation direct detection dark matter detectors through coherent elastic
neutrino-nucleus scattering (CE$\nu$NS) and elastic neutrino-electron
scattering (E$\nu$ES) measurements. Taking into account various details like
the quenching factor corrections, atomic binding effects, realistic
backgrounds, detection efficiency, energy resolution etc., we consider two
representative scenarios regarding detector specifications. For both scenarios,
we obtain the model-independent projected sensitivities for all possible
Lorentz-invariant interactions, namely scalar ($S$), pseudoscalar ($P$), vector
($V$), axial vector ($A$) and tensor ($T$). For the case of vector
interactions, we also focus on two concrete examples: the well-known
$U(1)_{B-L}$ and $U(1)_{L_\mu - L_\tau}$ gauge symmetries. For all interaction
channels $X=\{S,P,V,A,T\}$, our results imply that the upcoming dark matter
detectors have the potential to place competitive constraints, improved by
about 1 order of magnitude compared to existing ones from dedicated CE$\nu$NS
experiments, XENON1T, beam dump experiments and collider probes.
