  We introduce the notion of integrable modules over $\imath$quantum groups
(a.k.a. quantum symmetric pair coideal subalgebras). After determining a
presentation of such modules, we prove that each integrable module over a
quantum group is integrable when restricted to an $\imath$quantum group. As an
application, we show that the space of matrix coefficients of all simple
integrable modules over an $\imath$quantum group of finite type with specific
parameters coincides with Bao-Song's coordinate ring of the $\imath$quantum
group.
