Bent moved to Pride Park from Aston Villa in January, having fallen out of favour at the Premier League club.
The former England international has been in good form for table-toppers Derby, who are well-placed to atone for last season's agonising play-off final defeat, scoring seven goals in 10 appearances in all competitions.
However, it appears they will be shorn of his services until April.
"He had a scan on his hamstring and he will miss three to four weeks," said first-team coach Paul Simpson.
"We are having a disappointing run with injuries, so this is a time where the whole squad can play their part at an important time."
