Unlimited access to information and data sharing wherever and at any time for anyone and anything is a fundamental component of fifth-generation (5G) wireless communication and beyond. Therefore, it has become inevitable to exploit the super-high frequency (SHF) and millimeter-wave (mmWave) frequency bands for future wireless networks due to their attractive ability to provide extremely high data rates because of the availability of vast amounts of bandwidth. However, due to the characteristics and sensitivity of wireless signals to the propagation effects in these frequency bands, more accurate path loss prediction models are vital for the planning, evaluating, and optimizing future wireless communication networks. This paper presents and evaluates the performance of several well-known machine learning methods, including multiple linear regression (MLR), polynomial regression (PR), support vector regression (SVR), as well as the methods using decision trees (DT), random forests (RF), K-nearest neighbors (KNN), artificial neural networks (ANN), and artificial recurrent neural networks (RNN). RNNs are mainly based on long short-term memory (LSTM). The models are compared based on measurement data to provide the best fitting machine-learning-based path loss prediction models. The main results obtained from this study show that the best root-mean-square error (RMSE) performance is given by the ANN and RNN-LSTM methods, while the worst is for the MLR method. All the RMSE values for the given learning techniques are in the range of 0.0216 to 2.9008 dB. Furthermore, this work shows that the models (except for the MLR model) perform excellently in fitting actual measurement data for wireless communications in enclosed indoor environments since they provide R-squared and correlation values higher than 0.91 and 0.96, respectively. The paper shows that these learning methods could be used as accurate and stable models for predicting path loss in the mmWave frequency regime.