Multiple sclerosis (MS) is a chronic demyelinating condition characterized by plaques in the white matter of the central nervous system that can be detected using magnetic resonance imaging (MRI). Many deep learning models for automated MS detection based on MRI have been presented in the literature. We developed a computationally lightweight machine learning model for MS diagnosis using a novel handcrafted feature engineering approach. The study dataset comprised axial and sagittal brain MRI images that were prospectively acquired from 72 MS and 59 healthy subjects who attended the Ozal University Medical Faculty in 2021. The dataset was divided into three study subsets: axial images only (n = 1652), sagittal images only (n = 1775), and combined axial and sagittal images (n = 3427) of both MS and healthy classes. All images were resized to 224 × 224. Subsequently, the features were generated with a fixed-size patch-based (exemplar) feature extraction model based on local phase quantization (LPQ) with three-parameter settings. The resulting exemplar multiple parameters LPQ (ExMPLPQ) features were concatenated to form a large final feature vector. The top discriminative features were selected using iterative neighborhood component analysis (INCA). Finally, a k-nearest neighbor (kNN) algorithm, Fine kNN, was deployed to perform binary classification of the brain images into MS vs. healthy classes. The ExMPLPQ-based model attained 98.37%, 97.75%, and 98.22% binary classification accuracy rates for axial, sagittal, and hybrid datasets, respectively, using Fine kNN with 10-fold cross-validation. Furthermore, our model outperformed 19 established pre-trained deep learning models that were trained and tested with the same data. Unlike deep models, the ExMPLPQ-based model is computationally lightweight yet highly accurate. It has the potential to be implemented as an automated diagnostic tool to screen brain MRIs for white matter lesions in suspected MS patients.