Residual stress is a critical factor that influences the lifespan of mechanical components subjected to fatigue. Compressive stress tends to extend the life of a component, whereas tensile stress can shorten it. Acoustic emission (AE) signals have been linked to phenomena occurring during manufacturing processes; however, only a few studies have been conduct to correlate AE signals with the surface integrity of machined parts. In this study, an approach for correlating residual stress with AE signals is introduced. AISI 4340 steel specimens are machined by using ceramic tools, with varied cutting speeds, feed rates, and depths of cut, and AE signals are recorded during the process. The signals are processed and analyzed by using the spectral entropy technique, also known as Shannon entropy or information entropy. The results reveal that the appropriate application of frequency filters uncovers regions of strong correlation between the spectral entropy of the AE signals and the residual stress. The observed correlation can contribute to the optimization and control of machining processes and help to achieve the desired residual stress levels.