An automatic detection method for disease diagnosis plays an important role in the medical field. A computer-aided diagnosis (CAD) system for seizure detection using electroencephalogram (EEG) data is significant in protecting patients' lives. This paper presents machine learning algorithm-based seizure detection approach implemented in both software and hardware using EEG recordings. The input EEG signal is subjected to pre-processing, decomposition using wavelet transform and classification by a support vector machine (SVM) classifier. The maximum and variance statistical values of the decomposed EEG sub-bands are computed to generate a feature vector, while classification accuracy and computational complexity are taken into account. Gaussian Radial Basis Function (RBF) kernel based Non-Linear SVM (NLSVM) is used in this proposed approach to solve both two-class and three-class classification problems. In three-class classification, the one-against-one (OAO) technique is used. The competency of the proposed technique is evaluated using two distinct datasets provided by Bonn University, Germany & Neurology and Sleep Centre, New Delhi. The adequate parameters of the NLSVM classifier model are determined by using MATLAB software in the training phase and the best performing NLSVM model is selected for implementation on the Field-Programmable Gate Array (FPGA). The proposed seizure detection method is implemented with Verilog code and examined on a Xilinx Zynq-7000 XC7Z020 FPGA board to evaluate its performance. The experimental results show that the proposed method with a minimal number of features achieved a good performance metric for seizure detection and is comparable with that of the state-of-the-art methods.