The PHENIX experiment has measured $phi$ meson production in $d$$+$Au collisions at $sqrt{s_{_{NN}}}=200$ GeV using the dimuon and dielectron decay channels. The $phi$ meson is measured in the forward (backward) $d$-going (Au-going) direction, $1.2<y<2.2$ ($-2.2<y<-1.2$) in the transverse-momentum ($p_T$) range from 1--7 GeV/$c$, and at midrapidity $|y|<0.35$ in the $p_T$ range below 7 GeV/$c$. The $phi$ meson invariant yields and nuclear-modification factors as a function of $p_T$, rapidity, and centrality are reported. An enhancement of $phi$ meson production is observed in the Au-going direction, while suppression is seen in the $d$-going direction, and no modification is observed at midrapidity relative to the yield in $p$$+$$p$ collisions scaled by the number of binary collisions. Similar behavior was previously observed for inclusive charged hadrons and open heavy flavor indicating similar cold-nuclear-matter effects.