Early detection of water or steam leaks into sodium in the steam generator units of nuclear reactors is an important requirement from safety and economic considerations. Automated defect detection and classification algorithm for categorizing the defects in the steam generator tube (SGT) of nuclear power plants using magnetic flux leakage (MFL) technique has been developed. MFL detection is one of the most prevalent methods of pipeline inspection. Comsol 4.3a, a multiphysics modeling software has been used to obtain the simulated MFL defect images. Different thresholding methods are applied to segment the defect images. Performance metrics have been computed to identify the better segmentation technique. Shape-based feature sets such as area, perimeter, equivalent diameter, roundness, bounding box, circularity ratio and eccentricity for defect have been extracted as features for defect detection and classification. A feed forward neural network has been constructed and trained using a back-propagation algorithm. The shape features extracted from Tsallis entropy-based segmented MFL images have been used as inputs for training and recognizing shapes. The proposed method with Tsallis entropy segmentation and shape-based feature set has yielded the promising results with detection accuracy of 100% and average classification accuracy of 96.11%.