Understanding the amount of Soil Organic Carbon (SOC) at farm and field scale is a necessary precursor to effective management, important for both agricultural productivity and to reduce CO2 emissions. To avoid the prohibitive cost of measurement, SOC can be estimated by using multispectral images. In this study, we propose a novel Physics-Informed Convolutional Neural Network (CNN) to model well-known but noisy relationship between a soil index and SOC using the network’s loss function. This study is also conducted by resampling the European Land Use/Classification Area Survey (LUCAS) dataset to Sentinel-2 bands. Our experimental results show that our proposed network converges more quickly, has a lower root mean squared error (RMSE) and is more robust (as measured by the standard deviation of RMSE over multiple trials) than a compatible standard CNN. The operation of the novel Physics-Informed CNN is explained in terms of the components of the loss function.