The 28-year-old returned to training last week after three months out with a foot injury but broke down in an 11v11 game.
A specialist has told the centre back he now faces another six weeks on the sidelines.
Anderson, who joined Rovers from Burnley in 2018, is out of contract this summer.
“Tom’s obviously re-injured the area,” said McSheffrey. “It’s not as bad but the specialist has said it will be six weeks or so.
"So it looks for Tom as though his season’s done.
"I’m disappointed for Tom as a person and a player. Obviously you don’t want to be injured, and that goes for the rest of our injured players who have had a tough time of it this year.
"We support the players but we have to move on and get on with it and not dwell on it.
"We’ve got numbers in the building to deal with the situation we’re in. We just have to look forward and not dwell on what we can’t control.”
Left back Ben Jackson has trained this week after he was substituted in the first half of the defeat to Gillingham with a dead leg.
Ollie Younger suffered a dead leg in training last week and is hoping to be available against Fleetwood after sitting out last weekend.
John Bostock continued his road back to full fitness by playing for an hour in a practice game against Huddersfield Town earlier in the week.
Reo Griffiths has missed two weeks of training due to his Achilles tendon issue but trained today and could come into contention this weekend.
Cameron John is now doing some light training with a view to resuming full training at the end of this month.