With 41 minutes on the clock, Muamba fell face-down to the field near the midfield line without any players near him.
Medics rushed onto the field with a defibrillator and treated the 23 year old, pumping his chest for around six minutes of treatment before he was rushed to hospital.
Bolton manager Owen Coyle and striker Kevin Davies accompanied Muamba to hospital and Coyle later gave an update to Sky News saying, "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," Coyle said. "It's very serious. There's not getting away from that. He's critically ill and God willing he makes it through."
Tottenham released a statement after the match that read: "Tottenham can confirm that Fabrice Muamba has been taken to hospital following his collapse on the pitch during the match at White Hart Lane this evening.
"The match was immediately abandoned. Everyone at the club sends their best wished to Fabrice and his family."
Bolton had taken the lead during the match when Darren Pratley's header flew in off Gareth Bale's shoulder.
Tottenham equalised five minutes later when Kyle Walker powered home a Bale cross at the back post after 11 minutes.
Half an hour later the former England Under 21 international collapsed near the half-way line and play was suspended after 41 minutes.
Referee Howard Webb called the visibly shaken players off the field after consulting with managers Coyle and Harry Redknapp.
Paramedics used a defibrillator to try to resuscitate Muamba, who was wearing an oxygen mask and was flanked by a number of paramedics and Bolton medical staff as he left the pitch.
Both sets of fans sang Muamba's name as he lay on the pitch at the north London ground.
The announcement that the game had been called off was greeted with a round of applause from both ends.
Spurs player Rafael van der Vaart was one of the players on the pitch when Muamba collapsed. He tweeted: "Terrible what happened with Muamba during the game. We're all praying for him."
Soon after the incident, messages of support flooded in for the Bolton midfielder.
Middlesbrough defender Justin Hoyte, who came through the Arsenal youth team with Muamba, posted on his Twitter account: "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 teammate, Stuart Holden, wrote: "Praying for you Fab. Hope he's OK. Thoughts with him and his family."
Muamba started his career at Arsenal and spent two years at Birmingham before joining Bolton in 2008. He was born in Zaire but has represented England from Under 16 to Under 21 level.
Earlier yesterday, Everton forced Sunderland to a replay as the game finished 1-1 at Goodison Park.
In today's FA Cup quarter-finals, Stoke City face Liverpool while Chelsea entertain second-tier Championship side Leicester City.