The 27-year-old forward had just returned from a month out with a hamstring problem when he suffered an adductor injury after coming on as a substitute during last weekend’s 2-2 draw at Norwich.
Carroll has been beset by injury problems since joining the Hammers and has started just 31 Premier League games in two-and-a-half years.
But co-chairman David Gold hopes the latest setback will not mean another lengthy lay-off for their £15million club-record signing.
Gold revealed: “Andy has a slight injury and will be rested for the game against Blackburn.” Boss Slaven Bilic faces a striker shortage for the trip to Ewood Park after Enner Valencia was also injured against Norwich.
The Ecuador international limped off after sustaining an ankle knock midway through the second half at Carrow Road.
With Diafra Sakho still sidelined due to a thigh injury and Nikica Jelavic completing his move to Chinese second division side Beijing Renhe earlier this week, Bilic may have to throw January signing Emmanuel Emenike in for his full debut up front.
Bilic does have some positive fitness news, however, after Manuel Lanzini returned to training this week.
The Argentinian midfielder, who has scored four goals in 14 appearances this season, is available for the fifth-round clash with Rovers after six weeks out with a thigh injury.
Meanwhile Manchester United’s troubled season suffered another huge blow on Wednesday with the news that captain Wayne Rooney will be out for around six weeks with a knee injury.
The loss of Rooney - United’s leading scorer this season with 14 goals in all competitions, and seven in his last nine matches - is a major setback for boss Louis van Gaal at a time when his side are six points off the pace in the race for a top-four finish in the Premier League and his position is under increasing scrutiny.
Having allowed Danny Welbeck, Robin van Persie and Javier Hernandez to leave Old Trafford while James Wilson went on loan to Brighton, Van Gaal’s striking options now look very limited.
Compounding Van Gaal’s headaches is the fact that Marouane Fellaini has travelled to Belgium in a bid to cure a suspected hamstring injury.
United and Belgium are keen to get to the root of the injury, with the 28-year-old travelling to his homeland on Wednesday for check-ups with physio Lieven Maeschalck on a suspected tear.
Despite enduring a rocky relationship with United supporters, Fellaini has become a key figure for Van Gaal - starting 12 of the last 14 matches before his injury.