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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 (0.4M (circle dot)) and explosion energy (1.7 x 10(50) 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., Japan Society for the Promotion of Science (JSPS) through KAKENHI [JP17H02864, JP18H04585, JP18H05223, JP20H00174, JP20H04737, JP18H03720, JP16H02158]; Japan Society for the Promotion of Science [JP17K14253]; Turkish Scientific and Technical Research Council [TuBTAK-2211C, TuBTAK-2214A]; National Aeronautics and Space Administration, The authors acknowledge Raffaella Margutti, Dan Milisavljevic, and Wynn Jacobson-Galan for stimulating discussion, after their manuscript and this manuscript on SN 2019ehk were both posted on arXiv. The GMOS observation, S19A-051, was conducted via the time exchange program between Gemini and the Subaru Telescope. The FOCAS observation, S19B-055, was conducted at the Subaru Telescope, and the authors thank Kentaro Aoki and the Subaru telescope staff for the observation. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research has made use of the NASA/ IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Keiichi Maeda acknowledges support provided by the Japan Society for the Promotion of Science (JSPS) through KAKENHI Grants JP17H02864, JP18H04585, JP18H05223, JP20H00174, and JP20H04737. Masayuki Yamanaka is supported by the Grants-in-Aid for Young Scientists of the Japan Society for the Promotion of Science (JP17K14253). Koji S. Kawabata acknowledges support provided by the Japan Society for the Promotion of Science (JSPS) through KAKENHI Grant JP18H03720. Umut Burgaz acknowledges support provided by the Turkish Scientific and Technical Research Council (TuBTAK-2211C and 2214A) Tomoki Morokuma acknowledges support provided by the Japan Society for the Promotion of Science (JSPS) through KAKENHI Grants JP16H02158 and JP18H05223.