Keogh came off midway through the first half of the Rams' 3-1 victory over Rovers at the iPro Stadium on Saturday and was replaced at the heart of defence by on-loan Manchester United centre-back Michael Keane.
The 27-year-old jarred his right knee and the results of a scan have showed medial ligament damage. He is expected to be out for four weeks.
Derby head coach Steve McClaren sees Keogh's absence as a chance for Keane to show why he was brought to the club.
"One of the reasons we brought in Michael was for such a situation as this. We are lucky to have him here to step in when we have injuries," said McClaren on Saturday after leading the Rams to a seventh straight league win for the first time since the 1995/96 season.
"Now he gets a chance to show us what he can do, and I am sure he will take that opportunity.
"I don't think losing Richard impacted on us - I thought Michael came in and did very well. He did great and he has got to form a partnership with Jake Buxton now.
"You saw Michael and how composed and quick he is. He can come out with the ball and make us play football.
"He is also a real threat at set-pieces and should have scored with a couple of headers in the second half."
Derby face three Championship matches in seven days, starting away to Huddersfield on Boxing Day, and Keane is set to make his first start for the club after three substitute appearances.
The 20-year-old's loan spell ends after the home game against Wigan on New Year's Day but McClaren is hopeful of extending his stay for the rest of the season.