Leaf Area Index (LAI) and chlorophyll content are strongly related to plant development and productivity. Spatial and temporal estimates of these variables are essential for efficient and precise crop management. The availability of open-access data from the European Space Agency’s (ESA) Sentinel-2 satellite—delivering global coverage with an average 5-day revisit frequency at a spatial resolution of up to 10 metres—could provide estimates of these variables at unprecedented (i.e., sub-field) resolution. Using synthetic data, past research has demonstrated the potential of Sentinel-2 for estimating crop variables. Nonetheless, research involving a robust analysis of the Sentinel-2 bands for supporting agricultural applications is limited. We evaluated the potential of Sentinel-2 data for retrieving winter wheat LAI, leaf chlorophyll content (LCC) and canopy chlorophyll content (CCC). In coordination with destructive and non-destructive ground measurements, we acquired multispectral data from an Unmanned Aerial Vehicle (UAV)-mounted sensor measuring key Sentinel-2 spectral bands (443 to 865 nm). We applied Gaussian processes regression (GPR) machine learning to determine the most informative Sentinel-2 bands for retrieving each of the variables. We further evaluated the GPR model performance when propagating observation uncertainty. When applying the best-performing GPR models without propagating uncertainty, the retrievals had a high agreement with ground measurements—the mean R2 and normalised root-mean-square error (NRMSE) were 0.89 and 8.8%, respectively. When propagating uncertainty, the mean R2 and NRMSE were 0.82 and 11.9%, respectively. When accounting for measurement uncertainty in the estimation of LAI and CCC, the number of most informative Sentinel-2 bands was reduced from four to only two—the red-edge (705 nm) and near-infrared (865 nm) bands. This research demonstrates the value of the Sentinel-2 spectral characteristics for retrieving critical variables that can support more sustainable crop management practices.