The 23-year-old collapsed at Tottenham Hotspur's White Hart Lane stadium in London during an English FA Cup quarterfinal game and was treated by paramedics on the pitch.
He was subsequently taken to the London Chest Hospital where he has been in a critical condition since Saturday evening.
But a joint statement released by the hospital and Bolton on Monday evening said Muamba's condition had marginally improved.
It read: "Fabrice Muamba is continuing to show signs of improvement this evening.
"He is currently able to breathe independently without the aid of a ventilator. He has also been able to recognize family members and respond to questions appropriately.
"These are all positive signs of progress. However, his condition remains serious and the medical staff in intensive care will continue to monitor and treat him."
Muamba was born in Zaire but was brought up in the Democratic Republic of Congo. He moved to England when he was 11.
He represented England at under-21 level and has played for English Premier League side Arsenal, as well as Birmingham City, before moving to Bolton in 2008 for a fee of £5 million ($8 million).
He collapsed after 41 minutes of the last eight tie against Tottenham, with players from both sides urging medical assistance straight away.
Stunned supporters looked on as he was treated on the field while reports in the UK press claimed it took two hours for Muamba's heart to start beating normally again.
Referee Howard Webb abandoned the match after consultation with players and managers from both sides. Bolton's Premier League game with Aston Villa, scheduled for Tuesday, has also been called off.
Muamba's manager Owen Coyle has regularly visited the hospital where he is being treated, as have players from Bolton and other Premier League clubs.
Spanish club Real Madrid carried shirts that read "Get well soon Muamba" before their draw with Malaga on Sunday, and Coyle said the player's family were grateful for all the support they had received from around the globe.
"The message is the good will, the prayers from everybody, they are so thankful and they want to put that on record -- to say 'keep up the prayers, thanks for all the support,' " the Scot told reporters.
"They have been inundated as we all have, both in the football community globally and family and friends. People are taking a genuine interest and a real concern with how Fabrice is doing.
"It's a difficult situation but the family are bearing up as well as they can. They themselves are very positive people.
"You look at what Fabrice has been through in life already and you can tell that he is a fighter. He has such a fantastic smile and that's what we all want to see again."
Muamba's wife Shauna took to Twitter on Monday to say: "All your prayers are working people thank u so so much. Every prayer makes him stronger. "
There have been other cases of players collapsing during soccer matches. Motherwell's Phil O'Donnell suffered heart failure during a 2007 game against Scottish rivals Dundee United and died on the way to hospital.
The most high-profile tragedy of this kind came when Cameroon international Marc-Vivien Foe collapsed during a Confederations Cup semifinal against Colombia in 2003 and died in hospital.
There have been two similar incidents more recently in Spain, involving Sevilla's Antonio Puerta in 2007 and Espanyol's Daniel Jarque in 2009.
