The present paper deals with invariant submanifolds of CR-integrable almost Kenmotsu man-ifolds. Among others it is proved that every invariant submanifold of a CR-integrable (k, µ)-almost Kenmotsu manifold with k < −1 is totally geodesic. Finally, we construct an example of an invariant submanifold of a CR-integrable (k, µ)-almost Kenmotsu manifold which is totally geodesic.