We report here the first observation of directed flow (v_{1}) of the hypernuclei _{Λ}^{3}H and _{Λ}^{4}H in mid-central Au+Au collisions at sqrt[s_{NN}]=3 GeV at RHIC. These data are taken as part of the beam energy scan program carried out by the STAR experiment. From 165×10^{6} events in 5%-40% centrality, about 8400 _{Λ}^{3}H and 5200 _{Λ}^{4}H candidates are reconstructed through two- and three-body decay channels. We observe that these hypernuclei exhibit significant directed flow. Comparing to that of light nuclei, it is found that the midrapidity v_{1} slopes of _{Λ}^{3}H and _{Λ}^{4}H follow baryon number scaling, implying that the coalescence is the dominant mechanism for these hypernuclei production in the 3 GeV Au+Au collisions.