The Zaire-born England under-21 international fell face-down to the pitch near the halfway line without any players near him.
Medics rushed onto the pitch with a defibrillator and treated the 23-year-old Muamba, pumping his chest for around six minutes of treatment before he was rushed to hospital.
"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," Bolton said in a statement around three hours after the incident.
"No further information will be issued at this stage. The club has requested the media to respect his family's privacy at this time."
When Muamba collapsed in the 41st minute of the FA Cup match, Bolton manager Owen Coyle shouted from the touchline: "He's just collapsed."
Tottenham players William Gallas and Louis Saha along with referee Howard Webb immediately beckoned for medical support as the quarter-final was stopped.
Some players appeared to be praying as fans chanted Muamba's name between periods of complete silence at White Hart Lane.
After Muamba was carried off on a stretcher to applause from the crowd with an oxygen mask and with his chest still being pumped, all the players also left the pitch before Webb abandoned the match.
Coyle and striker Kevin Davies accompanied Muamba to hospital, while the rest of the squad returned to northwest England by train.
"Terrible what happened with Muamba during the game," Rafael van der Vaart, who started the game for Tottenham, wrote on Twitter. "We're all praying for him."
Muamba's Bolton teammate Stuart Holden, who was watching the game on television, tweeted: "Praying for you Fab."
"Waiting anxiously for updates from teammates," he added. "Fab is a fighter!"
Fabrice Ndala Muamba was born in what was then called Zaire on April 6, 1988. His father left the country because of political turmoil and settled in England, and Muamba joined Arsenal's youth academy in 2002.
He made his debut at age 17 on Oct. 25, 2005, in the League Cup at Sunderland, and was loaned to Birmingham in the League Championship the following season. The loan was made permanent in May 2007, and he made his Premier League debut for Birmingham in 2007-08 before joining Bolton in June 2008.
"I seriously hope my best friend in football is OK. Stay strong bro please please stay strong," said Middlesbrough defender Justin Hoyte, who came through the Arsenal youth team with Muamba.
Muamba has been part of England's youth team system and was a member of its team at last year's European Under-21 Championship, where he came on as a substitute against Ukraine and started against the Czech Republic.
"On behalf of The FA, I would like to send our thoughts and prayers to Fabrice Muamba and his family this evening," FA chairman David Bernstein said. "Fabrice has played 33 times for England Under-21s, captaining Stuart Pearce's side during this time and is a player, and more importantly, a person we care greatly for. We are in contact with Bolton Wanderers over Fabrice's condition and are awaiting updates."