Heaton was set to start the 2023-24 campaign as the club's number two goalkeeper behind Andre Onana, who made the move to Old Trafford from Inter Milan last month.
However, Man United revealed on Thursday evening that the 37-year-old has suffered an injury, believed to be related to his calf, which will keep him out of "the first few weeks of the season".
"Tom Heaton is out of Manchester United's Premier League season opener against Wolverhampton Wanderers at Old Trafford on Monday," read a statement on the club's official website.
"The experienced goalkeeper sustained an injury in training that is still being assessed but he is expected to be unavailable for the first few weeks of the season. We all wish Tom a speedy recovery."
As a result, Man United have a goalkeeping issue in the early stages of the season, with Onana the only senior stopper currently available for action, with Henderson not yet ready to return from a thigh injury.
Matej Kovar, 23, is still at the club, but the goalkeeper is thought to be nearing a move to Bayer Leverkusen, while Radek Vitek is also expected to leave on loan before the end of the window.
According to the Manchester Evening News, the news surrounding Heaton could lead to Henderson remaining at Old Trafford, at least until the January transfer window.
The England international joined Forest on loan last summer and made 20 appearances for the Reds in all competitions before picking up a season-ending thigh problem.
Forest have signed Matt Turner from Arsenal but are still said to be keen to bring in Henderson, potentially on loan with an option to buy.
Heaton's setback could lead to Henderson being kept on as back-up to Onana, though, even if the club are able to bring in another goalkeeper before the end of the transfer window.
Henderson was Man United's number one goalkeeper for a period of the 2020-21 campaign, making 26 appearances in all competitions for the 20-time English champions.
The 26-year-old has not featured during pre-season due to his thigh issue, and he will not be available for Monday's game against Wolves, which could potentially lead to Kovar's exit being delayed to ensure that there is adequate back-up to Onana for the campaign opener.