Leaf area index (LAI) and chlorophyll content, at leaf and canopy level, are important variables for agricultural applications because of their crucial role in photosynthesis and in plant functioning. The goal of this study was to test the hypothesis that LAI, leaf chlorophyll content (LCC), and canopy chlorophyll content (CCC) of a potato crop can be estimated by vegetation indices for the first time using Sentinel-2 satellite images. In 2016 ten plots of 30 × 30 m were designed in a potato field with different fertilization levels. During the growing season approximately 10 daily radiometric field measurements were used to determine LAI, LCC, and CCC. These radiometric determinations were extensively calibrated against LAI2000 and chlorophyll meter (SPAD, soil plant analysis development) measurements for potato crops grown in the years 2010-2014. Results for Sentinel-2 showed that the weighted difference vegetation index (WDVI) using bands at 10 m spatial resolution can be used for estimating the LAI (R 2 of 0.809; root mean square error of prediction (RMSEP) of 0.36). The ratio of the transformed chlorophyll in reflectance index and the optimized soil-adjusted vegetation index (TCARI/OSAVI) showed to be a good linear estimator of LCC at 20 m (R 2 of 0.696; RMSEP of 0.062 g·m −2 ). The performance of the chlorophyll vegetation index (CVI) at 10 m spatial resolution was slightly worse (R 2 of 0.656; RMSEP of 0.066 g·m −2 ) compared to TCARI/OSAVI. Finally, results showed that the green chlorophyll index (CI green ) was an accurate and linear estimator of CCC at 10 m (R 2 of 0.818; RMSEP of 0.29 g·m −2 ). Results for CI green were better than for the red-edge chlorophyll index (CI red-edge , R 2 of 0.576, RMSE of 0.43 g·m −2 ). Our results show that Sentinel-2 bands at 10 m spatial resolution are suitable for estimating LAI, LCC, and CCC, avoiding the need for red-edge bands that are only available at 20 m. This is an important finding for applying Sentinel-2 data in precision agriculture.