Binary classification of brain magnetic resonance (MR) images has made remarkable progress and many automated systems have been developed in the last decade. Multiclass classification of brain MR images is comparatively more challenging and has great clinical significance. Hence, it has recently become an active area of research in biomedical image processing. In this paper, an automated multiclass brain MR classification framework is proposed to categorize the MR images into five classes such as brain stroke, degenerative disease, infectious disease, brain tumor, and normal brain. A texture based feature descriptor is proposed using curvelet transform and Tsallis entropy to extract salient features from MR images. The potential of Tsallis entropy features is compared with Shannon entropy features. A kernel extension of random vector functional link network (KRVFL) is used to perform multiclass classification and improve the generalization performance at faster training speed. To validate the proposed method, two standard multiclass brain MR datasets (MD-1 and MD-2) are used. The proposed system obtained classification accuracies of 97.33% and 94.00% for MD-1 and MD-2 datasets respectively using 5-fold cross validation approach. The experimental results demonstrated the effectiveness of our system compared to the state-of-the-art schemes and hence, can be utilized as a supportive tool by physicians to verify their screening.