Morgan, who has recently been nursing a groin problem, lasted just 34 minutes on his return to the starting line-up against Stockport before he was forced off with another knock.
His anticipated absence is unlikely to be the only change made by boss John Sheridan.
Two games in the space of three days might be too much for Hatters hat-trick hero Jack Lester and the veteran striker will probably be rested. Therefore, either Jordan Bowery or Scott Boden could be recalled.
Ian Morris, Jack Hunt, Craig Clay and Deane Smalley are other options for Sheridan.