Alzheimer’s disease (AD) is a neurodegenerative brain disorder that affects cognitive functioning and memory. Current diagnostic tools, including neuroimaging techniques and cognitive questionnaires, present limitations such as invasiveness, high costs, and subjectivity. In recent years, interest has grown in using electroencephalography (EEG) for AD detection due to its non-invasiveness, low cost, and high temporal resolution. In this regard, this work introduces a novel metric for AD detection by using multiscale fuzzy entropy (MFE) to assess brain complexity, offering clinicians an objective, cost-effective diagnostic tool to aid early intervention and patient care. To this purpose, brain entropy patterns in different frequency bands for 35 healthy subjects (HS) and 35 AD patients were investigated. Then, based on the resulting MFE values, a specific detection algorithm, able to assess brain complexity abnormalities that are typical of AD, was developed and further validated on 24 EEG test recordings. This MFE-based method achieved an accuracy of 83% in differentiating between HS and AD, with a diagnostic odds ratio of 25, and a Matthews correlation coefficient of 0.67, indicating its viability for AD diagnosis. Furthermore, the algorithm showed potential for identifying anomalies in brain complexity when tested on a subject with mild cognitive impairment (MCI), warranting further investigation in future research.