The former Villa captain limped out of his side's 4-1 Capital One Cup victory over Norwich on Tuesday after just 35 minutes on the pitch.
Bent was replaced by Andreas Weimann, who went on to score twice, further damaging the England man's prospects of getting into Paul Lambert's XI.
Since losing the armband early in the season, Bent has fallen behind Christian Benteke in the attacking pecking order, playing just twice since October 30, and has been linked with a January move to QPR.
|12/1||Christian Benteke is 12/1 to score the first goal when Aston Villa take on Liverpool with bet365|
Lambert told reporters: "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."
The former Colchester boss also revealed that new skipper Ron Vlaar will undergo a scan on a calf injury that has sidelined him in recent weeks.