Absorption line series WJ(J=I,II,III,…) appeared below the indirect, edge in BiI3has been studied. The series is assigned to the excitons confined in mesoscopic domains produced by deformation faults characteristic of layered materials. Each line consists of four structures which correspond to x+iy, x-iy, z, and pure triplet states originated from the bulk cationic excitons. The energy separations between these four states are depend on the size of mesoscopic domains in which an exciton is confined. By introducing a disk-like shape model of the mesoscopic domain, the experimental results are analyzed on the basis of anisotropic quantum size effects on the cationic excitons. The relative motion of the exciton is found to be strongly affected by the localization of the translational motion in the direction perpendicular to the confinement axis.