The transverse momentum spectra of $D^0$ mesons from b hadron decays are measured at midrapidity ($|y|<1$) in pp and PbPb collisions at a nucleon--nucleon center of mass energy of 5.02 TeV with the CMS detector at the LHC. The $D^0$ mesons from b hadron decays are distinguished from prompt $D^0$ mesons by their decay topologies. In PbPb collisions, the $B \to D^{0}$ yield is found to be suppressed in the measured $p_T$ range from 2 to 100 GeV/$c$ as compared to pp collisions. The suppression is weaker than that of prompt $D^0$ mesons and charged hadrons for $p_T$ around 10 GeV/$c$. While theoretical calculations incorporating partonic energy loss in the quark-gluon plasma can successfully describe the measured $B \to D^{0}$ suppression at higher $p_T$, the data show an indication of larger suppression than the model predictions in the range of $2<p_{T}<5$ GeV/$c$.