Referee Howard Webb ended the match after 41 minutes after Muamba collapsed to the White Hart Lane pitch after suffering a cardiac arrest.
The 23-year-old received prolonged resuscitation on the pitch and in an ambulance en route to the London Chest Hospital where he remains in a critical condition.
Paramedics could not get Muamba's heart beating on its own for almost two hours.
A statement from the hospital and Bolton this morning also revealed Muamba, who is a father of one, would remain "anaesthetised in intensive care and will be for at least 24 hours".
The news has rocked the football world with Redknapp, who was standing on the touchline when Muamba collapsed, saying: "All our thoughts are with Fabrice, his family, (Bolton boss) Owen Coyle and the club.
"It was the right decision to abandon the game, everybody was in a state of shock and it wouldn't have been right to carry on.
"Football is the last thing on anyone's mind when an awful situation such as this happens. All we are thinking about now is Fabrice and his family."
The medical staff at White Hart Lane have been praised for the speed in which they tended to Muamba, while both sets of fans chanted his name as he received treatment on the pitch.
"We are immensely proud and grateful to the medical teams at both clubs, their response was immediate and professional," Spurs chairman Daniel Levy said.
"Our thanks also to both sets of fans for their support and behaviour. Too often we read the negatives about football and yet last night, at a time of intense emergency and uncertainty, we saw the true humanity and empathy of the footballing family."
He added: "Our thoughts are with Fabrice's family and Bolton Wanderers and we are all willing him to pull through. Events such as this put everything into perspective."
Muamba's former manager Steve Bruce admitted his shock after describing the midfielder as one of the fittest players he had ever managed.
Bruce signed Muamba for Birmingham from Arsenal in 2007,
"He had a fierce determination," Bruce told Radio Five Live's Sportsweek programme.
"He was as good as I've ever had in being able to get up and down the pitch. His fitness levels and the energy he brought to the team are quite remarkable.
"That's the unbelievable thing. He was a supremely fit young athlete.
"He's a tremendous lad. His greatest strength is his humbleness.
"It's quite unbelievable what has happened in the last 24 hours."
Worried fans and players took to Twitter to give their reaction to Muamba's collapse.
Middlesbrough defender Justin Hoyte, who came through the Arsenal youth team with Muamba, posted: "I seriously hope my best friend in football is OK. Stay strong bro please please stay strong. God is with you remember that."
Muamba's Bolton team-mate Stuart Holden wrote: "Praying for you Fab. Hope he's OK. Thoughts with him and his family."
Former Bolton boss Sam Allardyce, now at West Ham, relived a similar experience while he was also in charge of the Trotters in a Carling Cup tie with Spurs.
Senegal international Khalilou Fadiga collapsed prior to the match at the Reebok Stadium.
"He was diagnosed with a heart defect. He had a procedure that had said this heart defect had been rectified," Allardyce said.
"Unfortunately for us we had this experience where Kally collapsed in the warm-up before the game and his heart had actually stopped. I can remember it vividly.
"They had to 'defib' him there and then and get the heart re-started.
"Of course that was done expertly well by the medical staff and the doctor at Bolton."
Allardyce said Fadiga was able to play again, adding: "He was then taken to hospital and monitored and eventually he was fitted with a portable defibrillator, which was fitted under the chest bone so if he wanted to start playing football again, which he did.
"At Bolton he played a couple of games but then I think he went back to France and played there as well as Belgium. And now he is all fit and well."
Players and fans showed their support for Muamba with a minute's applause before Wolves' Premier League match against Manchester United at Molineux.
Chelsea's Gary Cahill - a team-mate of Muamba's before his transfer from Bolton in January - scored his side's opening goal against Leicester in their FA Cup quarter-final clash.
While celebrating his goal he lifted his shirt to reveal a T-shirt with the message: "Pray 4 Muamba."
Former Bolton captain Alan Stubbs, who made more than 200 appearances for Wanderers from 1990-96, said: "We're all hoping that we get positive news. We want Fabrice to come through this just as a person, not as a footballer.
"Football becomes nowhere near as important in this situation. Everyone's thoughts are with Fabrice and his family."
Stubbs, whose former Celtic team-mate Phil O'Donnell died from heart failure aged just 35 after collapsing while playing for Motherwell, added: "If we can detect this earlier in kids who are six, seven, eight then great but unfortunately there are going to be things that happen no matter what tests are done.
"I'm sure Fabrice would have had all the tests because footballers now get the best medical attention and facilities. It's just a sad situation."
Scotland manager Craig Levein also passed on his best wishes to Muamba and his family.
He said: "It's an unbelievably unusual situation. You look at him playing and it's difficult to understand how somebody as fit and healthy looking as him could have a problem.
"It just very much brings it home that we are all vulnerable."
Levein was Dundee United manager when O'Donnell collapsed during their game with Motherwell in 2007.
"It was a shock to everybody in Scotland," he said. "People still find it difficult to understand.
"There have been some great strides in recent years, particularly after the Phil O'Donnell situation, to screen every player but it shows you, how they are monitoring in the Premier League and the money invested, it's still very difficult to catch every problem."