The concept of eutectic solvents as a platform technology for a variety of applications including gas separation has become a popular approach. To date, the number of known deep eutectic solvents (DESs) is limited mainly to halide salts easily interacting with a hydrogen-bond donor (HBD) and resulting in the formation of a liquid phase. Actually, the DESs properties may be tuned by selecting the appropriate HBD, while the structure of the anion is not a decisive factor. However, the presence of other anions may be favorable for certain applications; therefore, expanding the range of deep eutectic solvents seems a relevant issue of chemistry and material science. In this study, we report the high absorption properties of the DES based on 1-butyl-3-methyl imidazolium methanesulfonate-urea toward ammonia. The structure features investigations have revealed the major contribution of C(2)-H to hydrogen bonding. To assess the possibility of selective separation, the solubility of ammonia and two acidic gases (H2S and CO2) in the absorbent has been measured. A superior gas sorption capacity was observed for ammonia, for which the Henry's law constant was equal to 1.52 bar. The obtained results exceeded the solubility data reported in the literature for various ILs containing hydrogen-donating groups. The DESs demonstrated lower yet acceptable solubility toward hydrogen sulfide, whereas the solubility of CO, was relatively poor. The thermostimulated desorption has demonstrated that the ability of gases to bind with DES molecules can be ranked as follows: NH3 > H2S > CO2. The physical sorption mechanism of ammonia, hydrogen sulfide, and carbon dioxide in the DES was proven by FTIR and thermal desorption analysis. The absorption was totally reversible, and the solubility of gases remains almost unchanged after three cycles.