The Zaire-born midfielder fell face-down to the pitch near the halfway line without any players near him in Saturday's game and medics rushed onto the pitch to begin resuscitating him.
As the FA Cup quarterfinal fixture was abandoned, the 23-year-old was rushed to the heart attack unit at the London Chest Hospital accompanied by Coyle and striker Kevin Davies.
"Fabrice is critically ill. The next 24 hours are going to be absolutely crucial," Coyle told Sky News television outside the hospital. "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."
Muamba has played 33 times for England's under-21 team.
When Muamba collapsed in the 41st minute of the FA Cup match, 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 quarterfinal was stopped and live television coverage turned away from the scene.
Some distressed players appeared to be praying and tearful as fans chanted Muamba's name between periods of complete silence at White Hart Lane.
The crowd rose in applause as Muamba was carried off on a stretcher wearing an oxygen mask, while still having his chest pumped. The players also left the pitch before Webb abandoned the match shortly after.
Former Arsenal teammate Johan Djourou wrote on Twitter that he had visited Muamba on Saturday night.
"Just left the hospital," he said. "Love you so much man! Keep fighting. Everybody please pray for him he's an amazing man and friend."
Tottenham striker Jermain Defoe, who played in Saturday's match, tweeted: "God willing he will pull through."
Muamba's Bolton teammate Stuart Holden, who was watching the game on television, tweeted: "Praying for you Fab."
"The guy is a fighter on and off the field. We love you bro," he added. "Waiting anxiously for updates from teammates."
Fabrice Ndala Muamba was born in what was then called Zaire on April 6, 1988. His father left the country for England because of political turmoil and his son joined him here in 1999.
"This is my adopted country," Fabrice Muamba said last year. "People have helped me, welcomed me with open arms and given me this opportunity. I'm earning a more than decent living and leading a comfortable life. I'm very appreciative of that."
The road to a professional footballing career started when he 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, a father of one, 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.
"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."
Premier League Chief Executive Richard Scudamore hailed Muamba as a "wonderful ambassador for the English game."
"We would like to praise the players, match officials, coaching staff and medical teams of both clubs at White Hart Lane for their swift actions in attending Fabrice," Scudamore added. "The league would also like to commend the compassion shown by the fans of Bolton Wanderers and Tottenham Hotspur."
There was an outpouring of support around the world for Muamba online and on pitches.
After scoring in a 5-0 win over Fiorentina in Italy's Serie A on Saturday evening, Juventus midfielder Andrea Pirlo dedicated the goal to Muamba.