A separation membrane complex includes a support that is porous, and a separation membrane with an amine supported on a surface thereof and in pores thereof in the vicinity of the surface, and the separation membrane complex is a membrane of a metal organic framework provided on the support and has a mean pore diameter of greater than or equal to 0.40 nm and less than or equal to 0.90 nm. In producing the separation membrane, an amine-containing solution is brought into contact with a surface of the membrane of the metal organic framework so that the amine is supported on the membrane.