Muamba was rushed to hospital after collapsing towards the end of the first half of an FA Cup quarter-final at Tottenham on Saturday.
It was later confirmed the 23-year-old had suffered a cardiac arrest.
A joint statement issued by the hospital and Bolton at 8.30pm local time (2030GMT) Sunday said: "Fabrice Muamba remains in a critical condition in intensive care in the Heart Attack Centre at the London Chest Hospital.
"There will be no further update tonight (Sunday)."
Bolton chairman Phil Gartside, after visiting Muamba in hospital with manager Owen Coyle on Sunday, released a statement, which read: "I know Fabrice's family have been overwhelmed by the huge outpouring of kindness, from people visiting the hospital to leave cards to those sending messages and emails.
"On behalf of our club, I would like to thank the Premier League, the FA and all the clubs who have been in touch to offer their support.
"This has extended worldwide with FIFA, UEFA and the global footballing family also."
Following Muamba's on-field collapse, World Cup final referee Howard Webb took the players off the field and then, with the agreement of both clubs, abandoned a tie where the score had stood at 1-1.
Tottenham and England striker Jermain Defoe, who was in tears when seeing Muamba lying on the pitch, visited him in hospital on Sunday but, still distressed, made no comment as he left.
Muamba's condition has also led Bolton to postpone their next match, a Premier League game away to Aston Villa due to take place on Tuesday.
Gartside thanked Bolton's rival top-flight teams in his statement by saying: "I would also like to offer our thanks and deep appreciation to all those at Tottenham Hotspur yesterday (Saturday) and Aston Villa for their understanding at this time.
"The staff at the London Chest Hospital have been nothing short of exceptional and I would like to thank them all at this on-going critical time.
"All BWFC (Bolton Wanderers Football Club) fans who have contacted me personally or the club have been unbelievable.
"We aspire to be a family and all expressions of support are testimony to the reality of the family club we have at Bolton. I ask for everybody to keep Fabrice in their prayers and thoughts."
As Bolton fans draped scarves and laid flowers outside the northwest side's Reebok Stadium home ground, supporters of other clubs paid tribute to Muamba with a minute's applause before kick-off in several matches on Sunday.
And during Chelsea's 5-2 FA Cup quarter-final win over Leicester, former Bolton defender Gary Cahill lifted his shirt to reveal a "Pray for Muamba" T-shirt after scoring the London club's first goal.
An earlier joint club/hospital statement confirmed the nature of Muamba's illness by saying he had been admitted after sustaining a "cardiac arrest".
It added: "Fabrice received prolonged resuscitation at the ground and on route to The London Chest Hospital, where his heart eventually started working.
"As is normal medical practice, Fabrice remains anaesthetised in intensive care and will be for at least 24 hours.
"His condition continues to be closely monitored by the cardiac specialists at the hospital."
That otherwise seemingly fit players could suffer cardiac problems while playing was brought home to the football world by the death of Cameroon's Marc-Vivien Foe during a Confederations Cup semi-final against Colombia in 2003.
And in 2004, Bolton's Senegal international Khalilou Fadiga, who subsequently recovered, collapsed before a League Cup tie against Tottenham at the Reebok with a heart problem.
Kinshasa-born Muamba moved to England from the Democratic Republic of Congo at the age of 11 after his father fled the war-torn country.
Source: PA
Source: PA