We measure the relative cross sections for D mesons produced in interactions of ${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{\ensuremath{\pi}}}^{+}$ beams with targets of Be, Cu, Al, and W. The measurement is based on 1400 fully reconstructed decays of the types ${\mathit{D}}^{0}$\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\pi}}}^{+}$, ${\mathit{D}}^{+}$\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\pi}}}^{+}$${\mathrm{\ensuremath{\pi}}}^{+}$, and charge conjugates. We find that the cross section for the production of both neutral and charged D's by either ${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$ or ${\mathrm{\ensuremath{\pi}}}^{+}$ is well fitted by the form ${\mathit{A}}^{\mathrm{\ensuremath{\alpha}}}$ where A is the atomic mass and \ensuremath{\alpha}=1.00\ifmmode\pm\else\textpm\fi{}0.05\ifmmode\pm\else\textpm\fi{}0.02, where the errors are statistical and systematic, respectively. There is no significant dependence of \ensuremath{\alpha} on the transverse or longitudinal momentum of the D meson or on the charge of either the incident pion or the produced D mesons.