We have investigated infrared transient absorption spectra under size-selective excitation of CuCl QDs embedded in NaCl matrices. The transient absorption consists of mainly two decay components. The spectra for the faster one, ascribed to the transition from the 1S-exciton to the 2P states, show a peak energy shift depending on the dot size. The results indicate that the Rydberg energy of the confined exciton has a size dependency. A comparison between the experimental data and a theoretical calculation has been carried out. The slower component does not depend much on the dot size and shows an anomalous long-lived time at low temperature. The properties of this slower component are also discussed.