The LEPS and CLAS data of the incoherent photoproduction of ϕ meson from deuteron at low energies are studied with a model for ϕ meson photoproduction from nucleon consisting of Pomeron, π, and η meson exchanges in the t-channel, and a postulated resonance, with parameters fitted to recent LEPS data on ϕ production from proton near threshold. The resonance was introduced to explain an observed bump in the forward differential cross section. Within impulse approximation, we find that the Fermi motion, final state interaction, and the resonance excitation all give important contributions to improve the agreement with data. However, discrepancies remain. Contributions from ϕ production via spectator nucleon by other mesons like π,ρ, and ϕ produced from the first nucleon need to be calculated in order to gain insight on the medium effects as well as the existence of the postulated nucleon resonance.