Leading 3-2 in the third set and with Simon serving, Djokovic lunged for a forehand shot and fell hard to the grass, rolling over and grabbing his upper-left arm and grimacing in pain.
But after receiving medical treatment, he recovered to play out the match. He broke Simon's serve in the final game, his seventh break in the match.
"It was a sharp pain," Djokovic said. "It was an awkward fall. I was just hoping there is nothing really bad with the joint. Luckily there is nothing damaged. I could play. Just the muscle was quite sore because of the impact. All in all, I'm just glad to get through."
Djokovic will play Jo-Wilfried Tsonga, who beat Jimmy Wang of Taiwan 6-2, 6-2, 7-5, in the fourth round. Including rain delays, Tsonga has played on all five days of the tournament.
"There is two days off, I'm going to try to recover and get ready," Djokovic said.
In other men's play, No. 19 Feliciano Lopez of Spain beat Ante Pavic of Croatia 6-4, 7-6 (4) 7-5 in a second-round match, and Kevin Anderson beat Fabio Fognini of Italy 4-6, 6-4, 2-6, 6-2, 6-1 to reach the fourth round.
Anderson, who won 10 of the last 11 games, is the first South African to advance to the fourth round at Wimbledon since Wayne Ferreira in 2000. He's reached the fourth round of his past three Grand Slams.
In a second-round match carried over from Thursday because of rain, Santiago Giraldo of Colombia beat No. 30 Marcel Granollers of Spain 4-6, 7-6 (2), 1-6, 6-1, 7-5, while 2013 semifinalist Jerzy Janowicz of Poland beat Australian veteran Lleyton Hewitt 7-5, 6-4, 6-7 (7), 4-6, 6-3.
Hewitt broke the Open era record for the most five-set matches played at Grand Slam tournaments. The loss to Janowicz was his 42nd five-set match, breaking the mark of 41 he had shared with Andre Agassi.
"I'd much rather win in three or four sets than go the distance all the time," Hewitt said about the record. "I seem to put everyone through the wringer quite a bit."
Hewitt, who was playing in his 61st Grand Slam tournament, gave a wave to the crowd at the end of the match and hinted at retirement during his post-match conference.
"You never know," he said. "I'm one injury away from hanging up the bats at any time."
Also going to five sets was No. 11 Grigor Dimitrov, who survived 21st-seeded Alexandr Dolgopolov, 6-7, 6-4, 2-6, 6-4, 6-1.
Later Friday, defending champion Andy Murray took a 15-match winning streak at the All England Club into the third round against 27th-seeded Roberto Bautista Agut of Spain.
Murray won six matches in a row at the venue to earn a gold medal at the 2012 London Olympics, then seven in a row during Wimbledon last year en route to the title, plus another two so far this week.
For complete Wimbledon coverage, including updated draws and reports from Steve Tignor, head to our tournament page.