Detonation initiation in a reactive medium can be achieved by an externally created shock wave. Supersonic flow onto a gravitating center, known as Bondi-Hoyle-Lyttleton (BHL) accretion, is a natural shock wave creating process, but, to our knowledge, a reactive medium has never been considered in the literature. Here, we conduct an order of magnitude analysis to investigate under which conditions the shock-induced reaction zone recouples to the shock front. We derive three semi-analytical criteria for self-sustained detonation ignition. We apply these criteria to the special situation where a primordial black hole (PBH) of asteroid mass traverses a carbon-oxygen white dwarf (WD). Since detonations in carbon-oxygen WDs are supposed to produce normal thermonuclear supernovae (SNe Ia), the observed SN Ia rate constrains the fraction of dark matter (DM) in the form of PBHs as log 10 (f pbh ) < 0.8 log 10 (m bh /g) − 18 in the range 10 21 − 10 22 g (10 20 − 10 22 g) from a conservative (optimistic) analysis. Most importantly, these encounters can account for both the rate and the median explosion mass of normal sub-Chandrasekhar SNe Ia if a significant fraction of DM is in the form of PBHs with mass 10 23 g.