The elliptic azimuthal anisotropy coefficient (v_{2}) is measured for charm (D^{0}) and strange (K_{S}^{0}, Λ, Ξ^{-}, and Ω^{-}) hadrons, using a data sample of p+Pb collisions collected by the CMS experiment, at a nucleon-nucleon center-of-mass energy of sqrt[s_{NN}]=8.16 TeV. A significant positive v_{2} signal from long-range azimuthal correlations is observed for all particle species in high-multiplicity p+Pb collisions. The measurement represents the first observation of possible long-range collectivity for open heavy flavor hadrons in small systems. The results suggest that charm quarks have a smaller v_{2} than the lighter quarks, probably reflecting a weaker collective behavior. This effect is not seen in the larger PbPb collision system at sqrt[s_{NN}]=5.02 TeV, also presented.