High impedance faults (HIFs) can lead to crucial damage to the utility grid, such as the risk of fire in material assets, electricity supply interruptions, and long service restoration times. Due to their low current magnitude, conventional protective equipment, such as overcurrent relays, cannot detect these faults. Alternatively, the waveform and variation range of current in HIFs are similar to other phenomena, such as linear and nonlinear load changes and capacitor banks. This paper employs a support vector machine (SVM) classification algorithm that demonstrates reliable accuracy and discrete wavelet transform (DWT) in HIF detection. First, the data set containing measured current signals of HIFs is collected to implement this approach. Then, DWT decomposes it to extract the features of each sample in the data set. The extracted features from this part are used as input to the SVM classification algorithm. The proposed idea is initially implemented on the IEEE 34-bus distribution test network. The proposed method achieves high capability and accuracy in detecting high-impedance faults. The proposed method is also applied to a real power distribution network in Markazi Province of Iran, yielding satisfactory results. EMTP-RV simulation software is used to simulate and evaluate the proposed method for power network modeling. Moreover, MATLAB software is used for feature extraction, and Python programming language in Google Colab and Spyder environment is applied to implement the SVM algorithm. The simulation results confirm the high accuracy of the suggested method. The main criteria obtained by the proposed method include accuracy, sensitivity, specificity, precision, F-score, and Dice, which are 99.581%, 98.684%, 100%, 100%, 99.338%, and 99.338%, respectively, for the test network, and 97.94%, 93.45%, 100%, 100%, 96.614%, and 96.618%, respectively, for the real power distribution network.