We present observations and modeling of SN 2016hnk, a Ca-rich supernova (SN) that is consistent with being the result of a He-shell double-detonation explosion of a C/O white dwarf. We find that SN 2016hnk is intrinsically red relative to typical thermonuclear SNe and has a relatively low peak luminosity ( M B = -15.4 mag), setting it apart from low-luminosity SNe Ia. SN 2016hnk has a fast-rising light curve that is consistent with other Ca-rich transients (t r = 15 days). We determine that SN 2016hnk produced 0.03 ± 0.01 M o˙ of 56Ni and 0.9 ± 0.3 M o˙ of ejecta. The photospheric spectra show strong, high-velocity Ca ii absorption and significant line blanketing at λ < 5000 Å, making it distinct from typical (SN 2005E-like) Ca-rich SNe. SN 2016hnk is remarkably similar to SN 2018byg, which was modeled as a He-shell double-detonation explosion. We demonstrate that the spectra and light curves of SN 2016hnk are well modeled by the detonation of a 0.02 M⊙ helium shell on the surface of a 0.85 M⊙ C/O white dwarf. This analysis highlights the second observed case of a He-shell double-detonation and suggests a specific thermonuclear explosion that is physically distinct from SNe that are defined simply by their low luminosities and strong [Ca ii] emission.