We present optical and near-infrared observations of SN 2019ehk, which was initially reported as a Type Ib supernova (SN). We show that it evolved to a Ca-rich transient according to its spectral properties and evolution in late phases. However, it shows a few properties distinct from those of the canonical Ca-rich transients: a short-duration first peak in the light curve, high peak luminosity, and association with a star-forming environment. Indeed, some of these features are shared with iPTF14gqr and iPTF16hgs, which are candidates for a special class of core-collapse SNe: the so-called ultra-stripped envelope SNe, i.e., a relatively low-mass He (or C+O) star explosion in a binary as a precursor of short-period double neutron star (NS) binaries. The estimated ejecta mass (0.4Me) and explosion energy (1.7 × 1050 erg) are consistent with this scenario. The analysis of the first peak suggests the existence of dense circumstellar material in the vicinity of the progenitor, implying a CCSN origin. Based on this analysis, we suggest SN 2019ehk is another candidate for a low-mass He star explosion. It might create a double NS binary, but with a wide separation. These candidates for low-mass stripped envelope SNe, including ultra-stripped envelope SN candidates, seem to form a subpopulation among Ca-rich transients, associated with young population. We propose that the key to distinguishing this population is the early first peak in their light curves.