Recent surveys have discovered a population of faint supernovae, known as Ca-rich gap transients, inferred to originate from explosive ignitions of white dwarfs. In addition to their unique spectra and luminosities, these supernovae have an unusual spatial distribution and are predominantly found at large distances from their presumed host galaxies. We show that the locations of Ca-rich gap transients are well matched to the distribution of dwarf spheroidal galaxies surrounding large galaxies, in a scenario where dark matter interactions induce thermonuclear explosions among low-mass white dwarfs that may be otherwise difficult to ignite with standard stellar or binary evolution mechanisms. A plausible candidate to explain the observed event rate are primordial black holes with masses above 1021 grams.