"He came to see me yesterday and said he wanted to quit. He didn't wish to go on," the club's chairman, Jean-Louis Campora, said yesterday. "Now we have to focus on the next match, at Lens on Saturday, which is far more important."
Tigana's duties have been taken on by the technical manager, Claude Puel, former goalkeeper Jean-Luc Ettori and the deputy coach, Jean Petit.
Petit said: "We have had to take emergency measures because nobody expected this. We needed to react swiftly."
Tigana, a former French international, joined Monaco as coach in July 1995 but has had a frustrating season.
Monaco are seventh in the French first division, 19 points behind the leaders, Marseilles, and out of contention for a place in the Champions' League next season. They were beaten in the Uefa Cup by Marseilles in December.
"This is the players' fault. We are responsible for what happened here [to Tigana]," the goalkeeper, Fabien Barthez, said. "But we must respect Tigana's decision."
Barthez is one of several players, including Thierry Henry and David Trezeguet, who have made it clear recently that they were unhappy and wanted to leave the club.
Tigana, capped 53 times, helped France to win the 1984 European title and played in two World Cup semi-finals in 1982 and 1986, both lost to Germany. He played for Toulouse, Lyon, Bordeaux and Marseilles before starting his coaching career in Lyon.
Dynamo Kiev have said they had cancelled the transfer of their Ukrainian international full-back, Oleh Luzhny, to Benfica because the Portuguese side had failed to to meet financial conditions. Luzhny had been on trial with Benfica during the Ukrainian close season but Dynamo accused them of a "lack of courtesy", causing "psychological damage" to the player. A Dynamo official had said Sheffield Wednesday might be interested in the defender.