The masses of the open charm ($D$ and $D^*$) mesons are investigated in the presence of strong magnetic fields. These are studied accounting for the mixing of the psuedoscalar and vector mesons, which is observed to lead to a drop (increase) in the mass of the $D$ (longitudinal component of $D^*$) meson. The charged $D$ and $D^*$ mesons, in addition, have the Landau level contributions in the presence of the magnetic field. The effects of the magnetic field on the decay wdiths of $D^*\rightarrow D\pi$ are studied using a field theoretic model of composite hadrons with quark/antiquark consittuents. The decay widths are computed using explicit constructions for the $D^*$, $D$ and the pion states in terms of the constituent quark fields. The matrix element for the decay $D^*\rightarrow D\pi$ is evaluated using the light quark--antiquark pair creation term of the free Dirac Hamiltonian for the constituent quark field. The modifications of the masses and decay widths of the open charm mesons in the presence of strong magnetic fields should have observable consequences on the production of the open charm ($D$ and $D^*$) mesons as well as of the charmonium states resulting from non-central ultrarelativistic heavy ion collision experiments.