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Let $m$ be a positive integer, $0<\alpha <mn$, $\overrightarrow{b}=(b_1,\cdots ,b_m)\in {\mathrm{BMO}}^m$. We give sufficient conditions on weights for the commutators of multilinear fractional integral operators ${ℐ}_{\alpha }^{\overrightarrow{b}}$ to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional type...