We present limits on spin-independent dark matter-nucleon interactions using a $10.6$ $mathrm{g}$ Si athermal phonon detector with a baseline energy resolution of $sigma_E=3.86 pm 0.04$ $(mathrm{stat.})^{+0.19}_{-0.00}$ $(mathrm{syst.})$ $mathrm{eV}$. This exclusion analysis sets the most stringent dark matter-nucleon scattering cross-section limits achieved by a cryogenic detector for dark matter particle masses from $93$ to $140$ $mathrm{MeV}/c^2$, with a raw exposure of $9.9$ $mathrm{g}cdotmathrm{d}$ acquired at an above-ground facility. This work illustrates the scientific potential of detectors with athermal phonon sensors with eV-scale energy resolution for future dark matter searches.