A functional polymer membrane of the present invention contains a polymer containing at least a structure represented by the following Formula (I), a method for producing the membrane, and an ion exchange apparatus: wherein R1 and R2 each represent a hydrogen atom or an alkyl group; R3 to R6 each represent a substituent; R3 to R6 may be bonded to each other and form a ring; A1 to A4 each represent a single bond or a divalent linking group; M1 represents a hydrogen ion, an organic base ion, or a metal ion; J1 represents a single bond, —O—, —S—, —SO2—, —CO—, —CR8R9—, or an alkenylene group, and R8 and R9 each represent a hydrogen atom, an alkyl group, or a halogen atom; and k1, k2, k3, k4, n1, n2, m1, m2, p, and q each represent a particular integer.