Muamba slumped to the turf in an FA Cup tie against Tottenham at White Hart Lane, and underwent several minutes of CPR and defibrillation before being taken to the London Chest Hospital.
"Bolton Wanderers can confirm that Fabrice Muamba has been admitted to the heart attack centre at London Chest hospital where he is currently in a critically ill condition in intensive care," the club said in a statement.
"No further information will be issued at this stage. The club has requested the media to respect his family's privacy at this time."
Sky News had reported a hospital spokesman as saying that he is breathing and in a stable condition.
The incident took place with nobody around him in the 42nd minute of the match, which was later abandoned by referee Howard Webb.
Medical staff spent several minutes attempting to resuscitate him using CPR and a defibrillator. Muamba was eventually carried from the pitch on a stretcher as doctors continued to attend to him.
Both sets of fans applauded him off, while players from both sides appeared greatly distressed.
Bolton later confirmed that the 23-year-old was taken to hospital. Manager Owen Coyle and club captain Kevin Davies are also understood to be there in support of the player.
Webb initially suspended the match pending further news on Muamba's condition, before it was confirmed that the game was abandoned.
Fans in the crowd looked visibly distraught as Muamba was being attended to. Some chanted his name, but in general White Hart Lane fell into a sombre silence.
Muamba was born in the Congolese capital of Kinshasa, but came to Britain at an early age with his family. He graduated through the youth ranks at Arsenal, and was a regular for England at Under-21 level.
Since joining Bolton from Birmingham City in 2008, Muamba has made 148 appearances for the Trotters.