The Irish star had worked himself back to fitness after a year out with a knee problem and lined-up for his first Premiership start since May 2001 in our opener at Everton on Saturday.
But his return lasted only 44 minutes when he collapsed clutching his hamstring after clearing the ball.
Early reports suggest he'll be out for four to six weeks and Glenn, who waited over year to partner Stephen and Christian Ziege together as wing-backs, has now lost the pair within 10 days.
"It's a bad tear," revealed boss Glenn after the 2-2 draw at Goodison Park. "It will be a minimum of four to six weeks if we're lucky.
"The lad has waited a whole year to play in the Premiership after a knee injury and now he's pulled his hamstring.
"That seems to be our luck at the moment on the injury front. It's been like that since I've been at the club. We'll have to deal with it and carry on. But I'm absolutely gutted for the lad."
A devastated Glenn Hoddle admits he is 'absolutely gutted' for injury-stricken Stephen Carr.