Bae had his overseas travel permit extension request rejected by the Military Manpower Administration on Monday, according to the Yonhap news agency.
All South Korean men between 18 and 35 must complete two years of military service, with the country still technically at war with North Korea after a peace treaty went unsigned following the 1950-53 Korean War.
The 28-year-old, who booked his ticket to the Masters with a win at the Frys.com Open in October, could face criminal charges if he doesn???t return to his home country within 30 days of his visa expiring.
However, the MMA can extend a person’s permit to stay overseas for up to three years if they have acquired permanent overseas residency and have lived for at least one year in that country.
Bae has spent 133 days non consecutively in South Korea over the past 12 months while enrolling in graduate school and playing in events on the Korean PGA Tour. The law firm representing the golfer, Jipyoung, is arguing the 133 days falls within the legal limit.
The two-time PGA Tour winner may also have the chance to avoid military service with the Korean government waiving the mandatory practice for any athlete who wins Asian Games gold or an Olympic medal.
Bae, who is the highest ranked Korean golfer at No 84 in the official world golf ranking,??would be expected to compete at the Rio Games in 2016 when the sport makes its return to the Olympics.
The 28-year-old, who has collected 14 wins as a professional worldwide, made his PGA Tour debut in 2012 and was granted US residency two years ago.