To investigate the quantum confinement effect on excitons in hybrid perovskites, single-crystal platelets of CH3NH3PbBr3 are grown on mica substrates using one-step chemical vapor deposition. Photoluminescence measurements reveal a monotonous blue shift with a decreasing platelet thickness, which is accompanied by a significant increase in exciton binding energy from approximately 70 to 150 meV. Those phenomena can be attributed to the one-dimensional (1D) quantum confinement effect in the two-dimensional platelets. Furthermore, we develop an analytical model to quantitatively elucidate the 1D confinement effect in such quantum wells with asymmetric barriers. Our analysis indicates that the exciton Bohr radius of single-crystal CH3NH3PbBr3 is compressed from 4.0 nm for the thick (26.2 nm) platelets to 2.2 nm for the thin (5.9 nm) ones. The critical understanding of the 1D quantum confinement effect and the development of a general model to elucidate the exciton properties of asymmetric semiconductor quantum wells pave the way toward developing high-performance optoelectronic heterostructures.