In previous years, Murray has been knocked out of the French tournament five times at the quarter-final stage.
Serbian star Djokovic defeated Stan Wawrinka 6-3, 3-6, 6-0 for his 21st straight win dating back to August 23.
The match marked a comeback for Djokovic, who lost the French Open final to Swiss player Wawrinka in June, which destroyed his chances of completing a career Grand Slam.
The Serb won this season’s Australian Open, US Open and Wimbledon – but was stopped in his tracks from becoming the third man, after Don Budge and Rod Laver, to win all four Grand Slam titles in the same year.
World number one Djokovic and second seed Murray have a long-standing rivalry. They have played each other 29 times on the ATP Tour, with Djokovic winning 20. The top seed has won almost all of his matches against the British player this year, winning five out of six, including a straight sets victory at the Shanghai Masters last month.
Paris is the last of the Masters 1000 series for the season. Djokovic has taken home five of the nine titles, while Murray has won two.