A 15-year-old boy developed a high fever and died three days after consuming the meat with two friends, local media reported.
The country’s National Centre for Zoonotic Diseases (NCZD) said the boy lived in the western Mongolian province of Govi-Altai.
Dozens of people who came into contact with the victim have been quarantined and authorities have issued warnings to China and Russia.
The bubonic plague is a bacterial disease spread by fleas living on rodents. Known as the “Black Death” in the Middle Ages, it is a highly infectious and often fatal condition.
Margaret Harris told a UN press briefing in Geneva: “We are monitoring the outbreaks in China, we are watching that closely and in partnership with the Chinese authorities and Mongolian authorities.
“At the moment we are not, considering it high-risk but we are watching it, monitoring it carefully,” she added.
Her comment came as local authorities in the city of Bayan Nur in the Chinese region of Inner Mongolia issued a warning after a hospital reported a case of suspected bubonic plague.
It followed four reported cases of plague in people there last November, including two of pneumonic plague, a deadlier variant.
The Tarbagan marmot, which is an endangered species, has been hunted for centuries in Mongolia and has been historically linked to plague outbreaks in the region.
Russia announced last week that it had stepped up patrols to stop people hunting marmots near its border with China and Mongolia.
Authorities in Russia’s Altai region, which borders Kazakhstan, China and Mongolia, said officials were patrolling the area to enforce a ban on hunting marmots and to warn people about the dangers, TASS news agency reported.