Bent has been out of favour under new boss Paul Lambert but made his return to the team in the midweek Capital One Cup victory at Norwich.
However, he limped out of what was his first game in six weeks after only half an hour.
The England international underwent a scan on Wednesday and Lambert is resigned to being without the club's record signing until the New Year.
Lambert said; "He went for a scan on Wednesday and he has got a problem with his hamstring which will keep him out for a few weeks.
"I think a few weeks. Maybe four weeks, I'd say, before we see him back."
Meanwhile, Villa skipper Ron Vlaar is to undergo a scan on Friday on the calf problem which has sidelined him for the past month.
Don't miss any live and exclusive football coverage this festive season. Click here to visit Sky Sports' Festive Calendar