An acute stressor can cause sleep disruptions. Electroencephalography (EEG) is one of the major tools to measure sleep. In rats, sleep stages are classified as rapid-eye movement (REM) sleep and non-rapid-eye movement (NREM) sleep, by different characteristics of EEGs. Sleep alterations after exposure to an acute stress are regularly determined by the power spectra of brain waves and the changes of vigilance stages, and they all depend on EEG analysis. Herein, we hypothesized that the Shannon entropy can be employed as an indicator to detect stress-induced sleep alterations, since we noticed that an acute stressor, the footshock stimulation, causes certain uniformity changes of the spectrograms during NREM and REM sleep in rats. The present study applied the Shannon entropy on three features of brain waves, including the amplitude, frequency, and oscillation phases, to measure the uniformities in the footshock-induced alterations of sleep EEGs. Our result suggests that the footshock stimuli resulted in a smoother and uniform amplitude as well as varied frequencies of EEG waveforms during REM sleep. In contrast, the EEGs during NREM sleep exhibited a smoother, but less uniform, amplitude after the footshock stimuli. The result depicts the change property of brain waves after exposure to an acute stressor and, also, demonstrates that the Shannon entropy could be used to detect EEG alteration in sleep disorders.