Duff missed the games against Millwall and Birmingham with a hamstring problem, only to return at Peterborough last week and suffer a calf injury which ruled him out of Saturday's 2-1 defeat at Bolton.
And, pending the results of a scan on Monday, the 35-year-old is likely to sit out the home games against Huddersfield and Middlesbrough, with his chances of returning for the trip to Brighton also in doubt.
"We are hopeful that it will be two to three weeks," Dyche told the club's official website.
"We will find out more from the scan, but he might be a few weeks or certainly a couple.
"We will see how it settles down, but he has been an important player for us and has done very well."
Northern Ireland international Duff has played a key role under Dyche, featuring in the side on six of the seven occasions the Clarets have kept a clean sheet since the ex-Watford boss took charge at the end of October.