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The rapid growth of hyperspectral satellite missions and the subsequent availability of hyperspectral images have encouraged the remote sensing community to investigate their potential in estimating the concentration of gases, such as methane (CH $_{ \boldsymbol {4}}$ ) and carbon dioxide (CO $_{ \boldsymbol {2}}$ ), which are related to the greenhouse effect. Though satellite hyperspectral sensors are not specifically designed for this purpose, they are expected to complement more specific satellite missions, such as NASA’s Orbiting Carbon Observatory -2 and -3 (OCO-2 and OCO-3), both in terms of enriched temporal sampling and improved spatial resolution. In this work, we present a new method to estimate the column-averaged dry-air mole fraction of CO $_{ \boldsymbol {2}}$ from hyperspectral data on a per-pixel basis. The method, which is here tailored to PRISMA images, leverages the spectral radiance samples collected in the short-wave InfraRed (SWIR) spectral region around the CO $_{ \boldsymbol {2}}$ absorption band at 2000 nm. By assuming a linear model to describe the dependence of the observed radiance on the CO $_{ \boldsymbol {2}}$ concentration, the estimation problem is reduced to matched filtering and can be effectively implemented in compliance with the low computational burden required to perform a pixel-by-pixel analysis. The performance of the presented method is investigated by means of a rigorous, physically based simulator that accurately reproduces the at-sensor radiance allowing one to check the validity of the assumptions and to assess the algorithm accuracy. The results show that the presented algorithm outperforms a benchmark continuum interpolated band ratio (CIBR)-based approach, which has been proposed in the literature to get fast per-pixel estimates of CO $_{ \boldsymbol {2}}$ concentration.