Fischer, in custody since he was detained by Japanese airport authorities on July 13 with an invalid U.S. passport, immediately appealed the decision.
The former chess great is wanted in the United States for violating international sanctions against Yugoslavia (search) in 1992, but he has alleged the charges against him are politically motivated.
The Justice Ministry would not say when Fischer would be deported, but ministry official Hideharu Maruyama said Fischer would most likely be sent to the United States.
"The justice minister's judgment was that there was no justification for Fischer's appeal," Maruyama said.
Fischer's lawyers said they had already filed suit in Tokyo District Court demanding that the order be canceled. His attorney, Masako Suzuki, said the court typically takes about one month to consider the written request for an injunction on the whole deportation process, supporters said.
The chess player's backers in Japan protested the ruling, saying the ministry officials who told Fischer of the decision said he would be deported later Tuesday.
"We managed to nip in the bud this fly-by-night effort to depart Bobby without due process," said John Bosnitch, a Tokyo-based advisor to Fischer.
Bosnitch accused the United States government of pressuring Japanese officials to speed proceedings against Fischer, but he said that would be much more difficult when the case moves to the courtroom.
"The court will now consider the request for the injunction. If that's granted, then nothing can happen," he said. "That's our desire, to effectively put the stopper in this bottle."
The deportation order is the latest development in Fischer's legal wrangle with Japanese authorities. In addition to appealing for asylum, Fischer has attempted to renounce his U.S. citizenship and announced plans to marry a Japanese woman in a bid to win sympathy from Tokyo.
Fischer rose to chess stardom by defeating Boris Spassky, formerly of the Soviet Union, in a series of games in 1972 to claim the world championship.
The chess legend, however, became increasingly erratic and reclusive after the Spassky match and lost his title as world champion in 1978.
In a 1992 rematch against Spassky, Fischer won and collected more than $3 million in prize money, violating U.N. sanctions by attending the match held in the former Yugoslavia.
In recent years, Fischer has emerged from silence in radio broadcasts and on his Web page to express anti-Semitic views and rail against the United States.
On a Web site Fischer's supporters acknowledge to be his home page, Fischer launches numerous attacks on Jews and decries the "international Jewish conspiracy" and "Jew-controlled U.S.," which he says are behind plots to both rule the world and ruin his life. At one point, the site denies the Holocaust.
Fischer's animosity toward his homeland is well-known, and he once praised the Sept. 11, 2001, terrorist attacks in a radio interview, saying America should be "wiped out."