Forest are among the main places on Earth where carbon is collected and accumulated. However, quantitative instrumental assessment of carbon fluxes is possible only for small-scale areas. When solving the scaling problem, we use machine learning methods, which can transform the values of the intensity of the Earth’s surface reflectance in different spectral intervals into ground-based in situ observations. The assessments of carbon fluxes by a regression neural network model of the multilayer perceptron type trained on FLUXNET network data for a station located in a boreal coniferous forest (56.4615°N, 32.9221°E) are presented. Using vegetation indicies NDVI and EVI measured by MODIS Aqua, air temperature at an altitude of 2 m, and total precipitation as input data, the model estimates of gross primary production (GPP), net ecosystem exchange (NEE), ecosystem respiration (TER), and some other parameters describing water and energy fluxes are calculated. Statistical estimation provides high values of the correlation coefficient and Nash-Sutcliffe coefficient on test dataset: R ≥ 0.9 and NSE ≥ 0.87 for GPP and TER; R = 0.4 and NSE = 0.15 for NEE.