Autism Spectrum Disorder (ASD) is a major incident neurological disorder. Medical practitioners use different diagnostic techniques such as Electroencephalogram (EEG) Analysis, Magnetic Resonance Imaging (MRI) analysis, and traditional Behavioral Analysis for ASD detection. However, diagnosis success largely depends on specialists' knowledge and remains seldom accessible to remote patients. To address this issue, recently, various machine learning (ML) approaches have been developed for ASD detection using brain MRI images. The performance of these approaches is often limited because of poor feature discrimination, inferior quality of features, high feature length, and poor correlation of features. Thus, there is a need for robust feature extraction and selection techniques to improve the performance of ASD detection. The proposed work demonstrates a fusion of three features, namely Gray Level Co-occurrence Matrix (GLCM) based holistic texture features, Local Binary Pattern (LBP) based local texture features, and Geometrical Features of the Corpus Callosum (GFCC) from brain MRI images. Further, a correlation-based feature selection technique is employed for the salient feature selection from the GLCM, LBP, and GFCC set to improve the feature quality. The effectiveness of the selected feature is evaluated using three ML classifiers such as K-Nearest neighbor (KNN), Support Vector Machine (SVM), and Classification Tree (CT). The proposed ASD detection scheme provides an accuracy of 95.86% with 10-fold cross-validation with a CT classifier. It is observed that the accuracy of the proposed system is improved by 11.32% over the recent GLCM-based ASD system. The correlation-based feature selection techniques minimize the recognition time by 34.95% over the ASD system without feature selection.