Many metaheuristic approaches have been developed to select effective features from different medical datasets in a feasible time. However, most of them cannot scale well to large medical datasets, where they fail to maximize the classification accuracy and simultaneously minimize the number of selected features. Therefore, this paper is devoted to developing an efficient binary version of the quantum-based avian navigation optimizer algorithm (QANA) named BQANA, utilizing the scalability of the QANA to effectively select the optimal feature subset from high-dimensional medical datasets using two different approaches. In the first approach, several binary versions of the QANA are developed using S-shaped, V-shaped, U-shaped, Z-shaped, and quadratic transfer functions to map the continuous solutions of the canonical QANA to binary ones. In the second approach, the QANA is mapped to binary space by converting each variable to 0 or 1 using a threshold. To evaluate the proposed algorithm, first, all binary versions of the QANA are assessed on different medical datasets with varied feature sizes, including Pima, HeartEW, Lymphography, SPECT Heart, PenglungEW, Parkinson, Colon, SRBCT, Leukemia, and Prostate tumor. The results show that the BQANA developed by the second approach is superior to other binary versions of the QANA to find the optimal feature subset from the medical datasets. Then, the BQANA was compared with nine well-known binary metaheuristic algorithms, and the results were statistically assessed using the Friedman test. The experimental and statistical results demonstrate that the proposed BQANA has merit for feature selection from medical datasets.