The dead man was named as John Byers. The ministry said three other tourists and the driver were injured in the incident yesterday morning.
A witness was reported as telling police that he saw three men wearing traditional robes open fire on the bus with machine guns.
Security sources said that Mr Byers was shot in the right side of the chest.
His wife, Linda Edwards, was slightly injured. Martine Morris, 47, had a fractured shoulder and her husband, Michael Morris, 46, suffered scratches to his back, the sources said, quoting Dr Daoud Nazeem of Naqada General Hospital.
The four Britons, all from London, had arrived in Egypt on 14 October and stayed in a hotel in Luxor. They had hired the minibus to go to Neqada in the southern province of Qena to see craftsmen weaving silk.
The ministry of the interior said in a statement that they were driving on a road which is not designated for tourist buses, and the driver, Ahmed Abdel-Kader, had not notified police of the journey. The statement said that the bus would have been given police protection had security officials been notified in advance.
The gunmen escaped and no one claimed responsibility for the attack, but security sources said that they believed the militant group al-Gamaa al-Islamiya (the Islamic Group) was responsible.
Mr Byers is the seventh foreign tourist to be killed since Islamic extremists launched a campaign of violence two and a half years ago to try to overthrow Egypt's government headed by President Hosni Mubarak and impose strict Islamic rule. A British nurse who was killed in southern Egypt on 21 October 1992 was the first tourist to die in the campaign.
Al-Gamaa has been the main force behind the radicals' campaign. It claimed responsibility for the death of a Spanish tourist in the same area in late August.
More than 435 people have been killed in the violence. The rebels' confrontation with the government was stepped up on 14 October, when the Nobel prize-winning author Naguib Mahfouz was injured in a knife attack on 14 October.
During the subsequent crackdown on the militants two policemen and 15 militants have died.
There have been 21 previous attacks on tourists in which six people have died and 50 have been injured. The attacks on foreign visitors have badly affected tourism, one of the government's main foreign currency earners.
A spokesman for the Foreign Office said it was not yet clear if Mr Byers was killed by bandits or if there was a political motive. He added:'The consul in Cairo is travelling to Luxor to help these people and will eventually be liaising with local police to find out the details.'