We report the first measurement of rapidity-odd directed flow (v_{1}) for D^{0} and D^{0}[over ¯] mesons at midrapidity (|y|<0.8) in Au+Au collisions at sqrt[s_{NN}]=200 GeV using the STAR detector at the Relativistic Heavy Ion Collider. In 10-80% Au+Au collisions, the slope of the v_{1} rapidity dependence (dv_{1}/dy), averaged over D^{0} and D^{0}[over ¯] mesons, is -0.080±0.017(stat)±0.016(syst) for transverse momentum p_{T} above 1.5 GeV/c. The absolute value of D^{0} meson dv_{1}/dy is about 25 times larger than that for charged kaons, with 3.4σ significance. These data give a unique insight into the initial tilt of the produced matter, and offer constraints on the geometric and transport parameters of the hot QCD medium created in relativistic heavy-ion collisions.