Muamba, 23, collapsed on the pitch during Saturday's FA Cup Quarter-Final against Spurs at White Hart Lane and is in a stable but critical condition in intensive care at the London Chest Hospital.
Tottenham's Premier League game against Stoke City on Wednesday will go ahead as planned. Manager Harry Redknapp said the incident, which led to the Bolton match being abandoned at 1-1 just before half-time, was a shock to everyone at his club.
"It is possible the effects of this could hit some quicker than others and despite these difficult circumstances we all have to pull together and carry on with our season," Redknapp told the club's website.
"We will be providing players with whatever support they need in order to help them move on from what has happened while obviously always keeping Fabrice at the forefront of our minds and willing him to make a recovery.
"We already had a cardiologist visiting the training ground today for routine screening so we are able to offer any player who wishes to be tested for the purpose of reassurance an additional opportunity to be screened."
It remains unclear why Muamba suffered a cardiac arrest but it is thought he did not suffer a heart attack.
According to the British Heart Foundation a cardiac arrest occurs when the heart stops pumping blood around the body, with the most common cause being an abnormal heart rhythm known as ventricular fibrillation.
A heart attack usually occurs due to coronary disease.
"This is a young and apparently fit individual who would probably represent the healthiest segment of society so what happened is very counter intuitive," Professor Sanjay Sharma told Sky News.
"It is very hard to imagine someone as fit as this could actually have a cardiac arrest on the pitch," added the professor, the consultant cardiologist who is screening the Spurs players.
The hospital said on Sunday that Muamba would remain anaesthetised for 24 hours.
Bolton manager Owen Coyle thanked hospital staff when he addressed waiting media on Monday.
"Their skills are incredible and we hope that it will help how quickly everyone reacted to the situation," he said.
"Today is a day when we wait and hope for improvement. He had such a fantastic smile and that's what we want to see again."
