Angular correlations between heavy-flavor decay electrons and charged particles at midrapidity (|η|<0.8) are measured in p-Pb collisions at sqrt[s_{NN}]=5.02 TeV. The analysis is carried out for the 0%-20% (high) and 60%-100% (low) multiplicity ranges. The jet contribution in the correlation distribution from high-multiplicity events is removed by subtracting the distribution from low-multiplicity events. An azimuthal modulation remains after removing the jet contribution, similar to previous observations in two-particle angular correlation measurements for light-flavor hadrons. A Fourier decomposition of the modulation results in a positive second-order coefficient (v_{2}) for heavy-flavor decay electrons in the transverse momentum interval 1.5<p_{T}<4 GeV/c in high-multiplicity events, with a significance larger than 5σ. The results are compared with those of charged particles at midrapidity and those of inclusive muons at forward rapidity. The v_{2} measurement of open heavy-flavor particles at midrapidity in small collision systems could provide crucial information to help interpret the anisotropies observed in such systems.