The Premier League club's doctor Jonathan Tobin told the BBC that 15 defibrillator shocks had failed to get the 23-year-old's heart beating in the hour after he collapsed on the pitch at Tottenham Hotspur.
"We were fearing the worst and didn't think we'd get the recovery we had. It's incredible," he said.
"It was 48 minutes when he collapsed to reaching hospital and a further 30 minutes after that. He was, in effect, dead at that time."
Tobin said he had gone out into the corridor and cried when the situation sank in after Muamba had arrived at the London Chest Hospital.
By Tuesday evening, however, the midfielder was sufficiently recovered to tell Tobin that he was feeling fine.
"I went to see Fabrice last night. I went in and he said 'Hi, doc.'," Sky television quoted Tobin as saying. "I asked him how he was and he said 'Fine'."
Andrew Deaner, a consultant cardiologist at the London hospital who was at White Hart Lane as a spectator and ran on to the pitch to help, said he had also been astonished by the player's recovery.
"If I was ever going to use the term miraculous it could be used here. He has made a remarkable recovery so far," he told the BBC.
"Two hours after [he had regained consciousness] I whispered in his ear, 'What's your name?' and he said, 'Fabrice Muamba'. I said 'I hear you're a really good footballer' and he said 'I try'. I had a tear in my eye."
Deaner said Muamba's life was not in danger now but it was too early to say whether he would be able to play again. Sam Mohiddin, the cardiologist looking after the player, said however that "normal life is within the spectrum of possibility."
The match against Tottenham was abandoned at 1-1 just before half-time and has been rescheduled for next Tuesday.
The Sun newspaper quoted a family friend reporting that Muamba had asked who won the match when he regained consciousness.
"He was told the match was called off while the two teams were drawing 1-1," said Aime Esalo. "Fabrice asked why they had stopped it and his father said 'Because of you'."
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