Individuals with mild cognitive impairment (MCI) are at high risk of developing into dementia (e. g., Alzheimer's disease, AD). A reliable and effective approach for early detection of MCI has become a critical challenge. Although compared with other costly or risky lab tests, electroencephalogram (EEG) seems to be an ideal alternative measure for early detection of MCI, searching for valid EEG features for classification between healthy controls (HCs) and individuals with MCI remains to be largely unexplored. Here, we design a novel feature extraction framework and propose that the spectral-power-based task-induced intra-subject variability extracted by this framework can be an encouraging candidate EEG feature for the early detection of MCI. In this framework, we extracted the task-induced intra-subject spectral power variability of resting-state EEGs (as measured by a between-run similarity) before and after participants performing cognitively exhausted working memory tasks as the candidate feature. The results from 74 participants (23 individuals with AD, 24 individuals with MCI, 27 HC) showed that the between-run similarity over the frontal and central scalp regions in the HC group is higher than that in the AD or MCI group. Furthermore, using a feature selection scheme and a support vector machine (SVM) classifier, the between-run similarity showed encouraging leave-one-participant-out cross-validation (LOPO-CV) classification performance for the classification between the MCI and HC (80.39%) groups and between the AD vs. HC groups (78%), and its classification performance is superior to other widely-used features such as spectral powers, coherence, and the complexity estimated by Katz's method extracted from single-run resting-state EEGs (a common approach in previous studies). The results based on LOPO-CV, therefore, suggest that the spectral-power-based task-induced intra-subject EEG variability extracted by the proposed feature extraction framework has the potential to serve as a neurophysiological feature for the early detection of MCI in individuals.