  Dark Matter (DM) particles with sufficiently large cross sections may scatter
as they travel through Earth's bulk. The corresponding changes in the DM flux
give rise to a characteristic daily modulation signal in detectors sensitive to
DM-electron interactions. Here, we report results obtained from the first
underground operation of the DAMIC-M prototype detector searching for such a
signal from DM with MeV-scale mass. A model-independent analysis finds no
modulation in the rate of 1$e^-$ events with periods in the range 1-48 h. We
then use these data to place exclusion limits on DM in the mass range [0.53,
2.7] MeV/c$^2$ interacting with electrons via a dark photon mediator. Taking
advantage of the time-dependent signal we improve by $\sim$2 orders of
magnitude on our previous limit obtained from the total rate of 1$e^-$ events,
using the same data set. This daily modulation search represents the current
strongest limit on DM-electron scattering via ultralight mediators for DM
masses around 1 MeV/c$^2$.
