In the framework of precision viticulture, satellite data have been demonstrated to significantly support many tasks. Specifically, they enable the rapid, large-scale estimation of some viticultural parameters like vine stem water potential (Ψstem) and intercepted solar radiation (ISR) that traditionally require time-consuming ground surveys. The practice of covering table grape vineyards with plastic films introduces an additional challenge for estimation, potentially affecting vine spectral responses and, consequently, the accuracy of estimations from satellites. This study aimed to address these challenges with a special focus on the exploitation of Sentinel-2 Level 2A and meteorological data to monitor a plastic-covered vineyard in Southern Italy. Estimates of Ψstem and ISR were obtained using different algorithms, namely, Ordinary Least Square (OLS), Multivariate Linear Regression (MLR), and machine learning (ML) techniques, which rely on Random Forest Regression, Support Vector Regression, and Partial Least Squares. The results proved that, despite the potential spectral interference from the plastic coverings, ISR and Ψstem can be locally estimated with a satisfying accuracy. In particular, (i) the OLS regression-based approach showed a good performance in providing accurate ISR estimates using the near-infrared spectral bands (RMSE < 8%), and (ii) the MLR and ML algorithms could estimate both the ISR and vine water status with a higher accuracy (RMSE < 7 for ISR and RMSE < 0.14 MPa for Ψstem). These results encourage the adoption of medium–high resolution multispectral satellite imagery for deriving satisfying estimates of key crop parameters even in anomalous situations like the ones where plastic films cover the monitored vineyard, thus marking a significant advancement in precision viticulture.