The 23-year-old collapsed in the 41st minute of Bolton's FA Cup quarter-final against Tottenham last night, with the match abandoned after the player received treatment on the pitch from paramedics.
Bolton manager Owen Coyle accompanied Muamba to the hospital and later emerged to give an update on the player's progress.
Owen Coyle: "Fabrice is critically ill. The next 24 hours are going to be absolutely crucial.
"We've obviously been inundated with people wishing him well and we hope that if everybody can pray strongly tonight that Fabrice is able to recover.
"It's very serious. There's not getting away from that. He's critically ill and God willing he makes it through."
A further update on the condition of Muamba will be released at some point later this morning.
Bolton last night released a statement which read: "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.
"No further information will be issued at this stage. The club has requested the media to respect his family's privacy at this time."
Within a second of seeing Muamba fall to the ground, Bolton manager Owen Coyle shouted "he's just collapsed" before running on to the pitch to be alongside his player amid a sombre atmosphere at Tottenham's ground.
Both sets of fans chanted the player's name as he was being treated and Tottenham forward Rafael van der Vaart and Muamba's team-mate Tuncay Sanli both prayed for the former Arsenal player on the pitch. Some fans cried at the sight of seeing a player out cold on the pitch.
Muamba was carried off on a stretcher and referee Howard Webb abandoned the match moments later.