Clement, a former assistant to Carlo Ancelotti at Chelsea and Real Madrid, had replaced fired former England manager Steve McClaren at the club in June.
Monday's dismissal was the Championship's 13th managerial casualty of the season. Rotherham United also fired Neil Redfearn on Monday.
"We are grateful for the contribution Paul has made to the football club but the time is right to make a change," chairman Mel Morris told the club website (www.dcfc.co.uk).
Derby are currently fifth in the Championship, five points behind leaders Hull City, but have gone seven league games without winning.
Morris said promotion this season to the Premier League, where clubs will share more money than ever next year under a new 5.1 billion pound ($7.35 billion) television deal, had not been the primary target.
"The priorities were building on the Derby way and style of football enjoyed in the past two seasons; adding depth and strength to our playing squad; and, developing and improving player and team performance.
"Sadly, on these measurements, we have not made enough progress and that is why we have decided to part company with Paul."
Twice English champions Derby were relegated from the top flight in 2008 following a dismal campaign in which they picked up only one win and recorded the lowest Premier League points total of 11.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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