The 21-year-old is expected to be out for up to eight weeks after suffering a torn hamstring in Saturday's 1-1 draw at Chelsea.
Anthony's season has been dogged by injuries. After a bright start, he was sidelined for almost two months with thigh trouble in September and then, just a game into his return, a knee problem kept him out for another 10 weeks.
He returned against Newcastle United last week and looked impressive alongside Ledley King at Stamford Bridge until his hamstring tear after 35 minutes.
"Anthony has torn his hamstring and that will be a minumum of six to eight weeks," said Glenn. "It's a shame for him because he was playing well and we keep losing him to injury.
"He hasn't managed to put three matches back-to-back for us. It's something we're aware of and we're trying to improve him but he's got a nasty injury there and he will be out for a while."
Glenn Hoddle feels full sympathy for luckless defender Anthony Gardner.