Henderson joined Forest on a season-long loan deal from Manchester United last summer, and he has gone to keep six clean sheets in 20 appearances.
However, the Man United loanee has not played since a 2-0 win over Leicester City on January 14 due to a thigh injury.
Despite travelling with the Forest squad for Saturday's 2-1 away defeat to Brentford, Henderson is set to miss the remainder of the 2022-23 campaign.
According to The Telegraph, the Forest goalkeeper has suffered a setback in his recovery and will miss the final four matches of the club's relegation fight.
Keylor Navas, who joined on loan from Paris Saint-Germain in January, will continue in goal for the rest of the season.
The Costa Rica international has put in a number of impressive performances, but he has also been susceptible to making errors during his time at the City Ground.
There was a suggestion from some quarters that he was at fault for Brentford's two late goals in Saturday's defeat to the West London club.
Forest boss Steve Cooper was asked after the game whether Navas could have done more to keep Brentford at bay.
"I just think that now is not the time to speak about anyone," Cooper told reporters. "It's about real togetherness and about sticking together."
News of Henderson's setback is another blow for a Forest squad that have been ravaged by injuries during the 2022-23 campaign.
Scott McKenna, Neco Williams, Willy Boly, Omar Richards and Chris Wood are all expected to miss the rest of the season.
Danilo scored at the Brentford Community Stadium, but he was later forced off and will now undergo a scan on a hamstring injury.
Forest are currently one point clear of the bottom three, but they are guaranteed to drop into the relegation zone following Monday's Premier League game between Everton and Leicester, who are both sitting in the relegation zone.