The structures in high-temperature environments are prone to undergo hardening and embrittlement as a result of thermal aging; this can cause variations in their mechanical properties. Because these changes occur at the microstructural level, it is difficult to evaluate them through linear ultrasonic techniques. In this work, a surface acoustic wave (SAW) was used to measure and compare the acoustic nonlinearity and mechanical properties of Al6061 alloys heat-treated at 220 °C for different durations (0 min, 20 min, 40 min, 1 h, 2 h, 10 h, 100 h, 1000 h). The SAW was generated by a pulsed laser and then received by an interferometer. Moreover, the yield strength, ultimate strength, and elongation to failure were measured by tensile tests. The results demonstrate that the critical variations in the mechanical properties can be detected by monitoring the variation features in the acoustic nonlinearity. Transmission electron microscopy images were captured to observe the microstructural changes, which shows that the acoustic nonlinearity varied according to the change in the precipitation phase. This supports the acoustic nonlinearity measurement using the laser-generated SAW being an effective technique for the fully noncontact nondestructive evaluation of material degradations as well as changes in mechanical properties.