We explore the prospect of constraining light mediators at the next generation direct detection dark matter detectors through coherent elastic neutrino-nucleus scattering ($\mathrm{CE}\ensuremath{\nu}\mathrm{NS}$) and elastic neutrino-electron scattering ($\mathrm{E}\ensuremath{\nu}\mathrm{ES}$) 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 $U(1{)}_{B\ensuremath{-}L}$ and $U(1{)}_{{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}}$ 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 $\mathrm{CE}\ensuremath{\nu}\mathrm{NS}$ experiments, XENON1T, beam dump experiments, and collider probes.