The PHENIX experiment at the Relativistic Heavy Ion Collider has measured phi meson production and its nuclear modification in asymmetric Cu + Au heavy-ion collisions at root s(NN) = 200 GeV at both forward Cu-going direction (1.2 < y < 2.2) and backward Au-going direction (-2.2 < y < -1.2) rapidities. The measurements are performed via the dimuon decay channel and reported as a function of the number of participating nucleons, rapidity, and transverse momentum. In the most central events, 0%-20% centrality, the phi meson yield integrated over 1 < pT < 5 GeV/c prefers a smaller value, which means a larger nuclear modification, in the Cu-going direction compared to the Au-going direction. Additionally, the nuclear-modification factor in Cu + Au collisions averaged over all centrality is measured to be similar to the previous PHENIX result in d + Au collisions for these rapidities.