The power generation by solar photovoltaic (PV) systems will become an important and reliable source in the future. Therefore, this aspect has received great attention from researchers, who have investigated accurate and credible models to predict the power output of PV modules. This prediction is very important in the planning of short-term resources, the management of energy distribution, and the operation security for PV systems. This paper aims to explore the sensitivity of Nonlinear Autoregressive Exogenous Inputs (NARX) and an Artificial Neural Network (ANNs) as a result of weather dynamics in the very short term for predicting the power output of PV modules. This goal was achieved based on an experimental dataset for the power output of a PV module obtained during the sunny days in summer and cloudy days in winter, and using the data in the algorithm models of NARX and ANN. In addition, the analysis results of the NARX model were compared with those of the static ANN model to measure the accuracy and superiority of the nonlinear model. The results showed that the NARX model offers very good estimates and is efficient in predicting the power output of the PV module in the very short term. Thus, the coefficient of determination (R2) and mean square error (MSE) were 94.4–97.9% and 0.08261–0.04613, respectively, during the summer days, and the R2 and MSE were 90.1–89.2% and 0.281–0.249, respectively, during the winter days. Overall, it can be concluded that the sensitivity of the NARX model is more accurate in the summer days than the winter days, when the weather conditions are more stable with a gradual change. Moreover, the effectiveness of the NARX model has the specificity to learn and to generalize more effectively than the static ANN.