Optical emission of the heterostructured GaAs/AlGaAs core/shell nanowires with a multiple quantum well structure of the shell was found dominant by spatially indirect recombination of the electrons in the NW core with the photoexcited holes confined in the QWs of the shell. Multiple photoluminescence peak structure corresponding to the contributions of the individual quantum wells was observed. Numerical calculations of the confined hole eigenstate energies allowed for determination of the characteristic parameters of the studied nanowires, such as the surface depletion potential, intrinsic electron concentration and the actual widths of the quantum wells and the barriers formed in the nanowire shell. The presented data suggest formation of highly uniform cylinder symmetry two-dimensional quantum wells embedded in the nanowire shell.