FIFA said Park Jong-woo was guilty of unsporting behaviour which "cannot be tolerated," and formally warned the Korea Football Association.
The International Olympic Committee can now decide if Park will get his medal which has been withheld since the Aug. 10 incident.
FIFA and the IOC prohibit on-field political statements.
After South Korea beat Japan 2-0 at Cardiff, Park displayed a sign in national colours with the slogan "Dokdo is our territory" to support sovereignty over islets which Japan also claims in a decades-old dispute.
In defending Park, Korean officials argued that he simply picked up the banner which was thrown from the stands.
FIFA said its disciplinary panel "took into account that the behaviour of the player, even though it appears not to have been premeditated or intentional, contradicts the principal idea and goal of sportsmanship and fair play, and therefore, cannot be tolerated."
Weeks after the controversy, the 23-year-old midfielder was called into the senior national team for 2014 World Cup qualifiers.
Park, who plays for Busan IPark, will serve his suspension when South Korea plays at home to Qatar on March 26 and away to Lebanon on June 4. FIFA also fined him 3,500 Swiss francs ($3,780).
FIFA rules prevent him appealing this sanction.
FIFA also reminded the Korean football association "of its obligation to properly instruct its players" about competition rules.
"The Korea Football Association was warned that should incidents of such nature occur again in the future, the FIFA Disciplinary Committee may impose harsher sanctions," the governing body said.
South Korea and Japan played the match in Wales amid sensitive diplomatic relations at home. Hours earlier, South Korea President Lee Myung-bak travelled to the islets where his country stations a small contingent of police officers in a show of control. The presidential visit prompted Japan to recall its ambassador from Seoul.
Japanese Foreign Minister Koichiro Gemba said it was "incomprehensible" why Lee would make the trip.