Midfielder Park Jong-woo is being investigated by the IOC and FIFA for carrying the sign with a slogan supporting South Korean sovereignty of islets which are disputed territory with Japan.
"We have also requested that the (South Korea Olympic Committee) takes swift action on this issue and that the athlete not be present at today's medal presentation ceremony," the IOC said in a statement. "We have opened an inquiry and have asked the (South Korea Olympic Committee) for an explanation."
Medals were presented at Wembley Stadium in London following Mexico's 2-1 win over Brazil in the gold-medal match. Only 17 of the 18 players were on the field for South Korea during the bronze presentations, and Park was not among them.
FIFA said it has opened a separate investigation to discipline Park.
The Olympic Charter and FIFA statutes prohibit political statements by athletes and players.
South Korea won 2-0 on Friday, hours after President Lee Myung-bak raised diplomatic tensions by travelling to the islets.
The presidential visit prompted Japan to recall its ambassador from Seoul.
The bronze-medal match in Cardiff, Wales, was seen as potentially further inflaming tensions.
FIFA has received pictures from the stadium showing a player celebrating victory with the sign on the field.
"The image will be passed to the chairman of the FIFA Disciplinary Committee for his review, and to evaluate any further steps to be taken," the football governing body said.
The largely uninhabited islets are called Dokdo in South Korean and Takeshima in Japanese.
South Korea stations a small contingent of police officers there in a show of control, but Japan maintains that the rocks are its territory. Tokyo renewed the claim last month in an annual defence report.
During his visit Friday, Lee reportedly told police officers there that the islets are "worth sacrificing lives for," according to the presidential office.
Japanese Foreign Minister Koichiro Gemba said it was "incomprehensible why (Lee) would make this trip at this time,"
Next Wednesday, South Korea will commemorate the peninsula's independence in 1945 from 35 years of Japanese colonial rule.