In any multi-script environment, handwritten script classification is an unavoidable pre-requisite before the document images are fed to their respective Optical Character Recognition (OCR) engines. Over the years, this complex pattern classification problem has been solved by researchers proposing various feature vectors mostly having large dimensions, thereby increasing the computation complexity of the whole classification model. Feature Selection (FS) can serve as an intermediate step to reduce the size of the feature vectors by restricting them only to the essential and relevant features. In the present work, we have addressed this issue by introducing a new FS algorithm, called Hybrid Swarm and Gravitation-based FS (HSGFS). This algorithm has been applied over three feature vectors introduced in the literature recently—Distance-Hough Transform (DHT), Histogram of Oriented Gradients (HOG), and Modified log-Gabor (MLG) filter Transform. Three state-of-the-art classifiers, namely, Multi-Layer Perceptron (MLP), K-Nearest Neighbour (KNN), and Support Vector Machine (SVM), are used to evaluate the optimal subset of features generated by the proposed FS model. Handwritten datasets at block, text line, and word level, consisting of officially recognized 12 Indic scripts, are prepared for experimentation. An average improvement in the range of 2–5% is achieved in the classification accuracy by utilizing only about 75–80% of the original feature vectors on all three datasets. The proposed method also shows better performance when compared to some popularly used FS models. The codes used for implementing HSGFS can be found in the following Github link: https://github.com/Ritam-Guha/HSGFS.