Bent limped out of the quarter-final tie at Carrow Road after only half an hour - his first start for six weeks.
The England international underwent a scan on Wednesday and Villa manager Paul Lambert is resigned to being without the club's record signing "for a few weeks".
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.
Asked if he was out of the Christmas matches, the Scot added: "Yes, probably, the way it is looking, yes.
"I think a few weeks. Maybe four weeks, I'd say, before we see him back."
It is another setback for Bent in a year to forget which saw him start as England's number one striker but lose his place in the first XI at Villa this season.
An ankle injury ruled him out of the final three months of last season and Euro 2012.
Bent started the new campaign in the Villa line-up but a further ankle setback and the form of Christian Benteke meant he slipped down the pecking order.
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