Timely crop yield information is needed for agricultural land management and food security. We investigated using remote sensing data from the Earth observation mission Sentinel-2 to monitor the crop phenology and predict the crop yield of sunflowers at the field scale. Ten sunflower fields in Mezőhegyes, southeastern Hungary, were monitored in 2021, and the crop yield was measured by a combine harvester. Images from Sentinel-2 were collected throughout the monitoring period, and vegetation indices (VIs) were extracted to monitor the crop growth. Multiple linear regression and two different machine learning approaches were applied to predicting the crop yield, and the best-performing one was selected for further analysis. The results were as follows. The VIs showed the highest correlation with the crop yield (R > 0.6) during the inflorescence emergence stage. The most suitable time for predicting the crop yield was 86–116 days after sowing. Random forest regression (RFR) was the best machine learning approach for predicting field-scale variability of the crop yield (R2 ∼ 0.6 and RMSE 0.284–0.473 t/ha). Our results can be used to develop a timely and robust prediction method for sunflower crop yields at the field scale to support decision-making by policymakers regarding food security.