An Fe-embedded C2N monolayer as a promising single-atom catalyst for CO oxidation by O2 has been investigated based on first-principles calculations. It is found that the single Fe atom can be strongly trapped in the cavity of the C2N monolayer with a large adsorption energy of 4.55 eV and a high diffusion barrier of at least 3.00 eV to leave the cavity, indicating that Fe should exist in the isolated single-atom form. Due to the localized metal 3d orbitals near the Fermi level, the embedded Fe single-atom catalyst has a high chemical activity for the adsorption of CO and O2 molecules. CO oxidation by O2 on the catalyst would proceed via a two-step mechanism. The first step of the CO oxidation reaction has been studied via the Langmuir-Hinshelwood and Eley-Rideal mechanisms with energy barriers of 0.46 and 0.65 eV, respectively. The second step of the CO oxidation reaction follows the Eley-Rideal mechanism with a much smaller energy barrier of 0.24 eV. For both the steps, the CO2 molecules produced are weakly adsorbed on the substrates, suggesting that the proposed catalyst will not be poisoned by the generated CO2. Our results indicate that the Fe-embedded C2N monolayer is a promising single-atom catalyst for CO oxidation by O2 at low temperatures.