But the Briton was outclassed from the start by defending champion Djokovic.
Edmund's defeat means Andy Murray is the last Briton left in the singles, while Djokovic goes on to face France's Jo-Wilfried Tsonga in the last eight.
Djokovic showed no signs of being rusty despite only completing six games in the past two rounds because of injuries to Jiri Vesely and Mikhail Youzhny.
The 29-year-old Serb needed treatment during the third set as the trouble he had with his upper arm in the first round flared up again.
But he came through unscathed to ensure his quest for a 13th Grand Slam title and third this year remains on track.
"It feels great to play a full match after a weird couple of days when I didn't have too much tennis," said Djokovic.
"I came out of the blocks with high intensity. It's not easy to do that when you have to wait all day to play.
"I made Kyle work for each point and kept him moving around the court."
Edmund's run to the fourth round - the best Grand Slam performance of his career so far - included victories over 13th seed Richard Gasquet and 20th seed John Isner.
