The top-ranked Serb slipped near the end of the second set and needed treatment for several minutes on his right groin area.
Serena Williams also had a fright, but she avoided a repeat second-round exit by beating Anna-Lena Friedsam of Germany, 5-7, 6-3, 6-3.
Djokovic followed Williams on Court Suzanne Lenglen and fans were treated to some more drama.
As he prepared to serve for the second set, Djokovic sat in his chair and called for medical assistance. Moments earlier, his left foot had slipped as he played a shot from the back of the court, throwing the weight of his body onto his right leg.
After receiving treatment, Djokovic pulled out a towel and unfurled it on the clay. With his orange shirt, he looked almost camouflaged as he lay on his back, before flipping over to his front.
“I slipped a lot and felt pain in the right leg,” Djokovic said. “But I'm not worried about it.”
He was more concerned about a careless mistake in the third set when, casually waiting for Muller's shot to land out, he let the ball glance off his racket and lost the point.
“I'm expecting a long talk with my two coaches,” he said. “I lost focus a bit. It's the first time this has happened in my career.”
The sixth-seeded Nadal, who stood out on center court dressed in electric blue in somewhat gloomy and overcast conditions, was not always at his best during his 6-4, 6-3, 6-1 win over Nicolas Almagro of Spain.
“The score is easier than what the match was like,” said Nadal, who will next play Andrey Kuznetsov of Russia. “My footwork was better. I felt better than during the first round.”
The third-seeded Murray beat Joao Sousa of Portugal, 6-2, 4-6, 6-4, 6-1.
Murray, who was recently married back home in Scotland in traditional tartan attire, looked stunned when he was interviewed by former player Fabrice Santoro afterward. That was because the Frenchman was dressed up as a Scotsman, with a kilt, a sporran, and long socks on.
“I don't really know what to say,” said Murray, as he stared amusedly at Santoro, before breaking out into laughter.
Williams had little to laugh about.
Seeking a 20th career major title and third at Roland Garros, dropped her serve four times in her first match against Friedsam, ranked 105th.
The Australian Open champion set up match point when she sent a huge forehand winner from the back of the court and followed that with another big, cross-court forehand winner
“I know I'm capable of playing great tennis, just haven't seen it yet,” said Williams, who lost in the second round last year.
“My level is literally a hundred times better than I played today,” Williams said. “I think I take more solace in the fact I can play better as opposed to the fact that that's the best I could play. Then I would be in trouble.”
Williams will next face Victoria Azarenka of Belarus after she beat Czech player Lucie Hradecka 6-2, 6-3.
At the 2011 Australian Open, Schiavone beat the Russian in the longest women's match, by time, in Grand Slam history — a 6-4, 1-6, 16-14 contest that lasted 4:44.
Earlier, fifth-seeded Caroline Wozniacki of Denmark was knocked out in the second round after losing to Julia Goerges of Germany 6-4, 7-6 (4).
In the men's side of the draw, fifth-seeded Kei Nishikori of Japan became the first player to reach the second week of the tournament. He was supposed to play Benjamin Becker in the third round on Friday, but Becker pulled out of the tournament because of a muscle tear in his right shoulder.
Other men's winners included U.S. Open champion Marin Cilic of Croatia, Leonardo Mayer of Argentina, Pablo Andujar of Spain, Jeremy Chardy of France — who beat 16th-seeded American John Isner — and Thanasi Kokkinakis of Australia.
Kokkinakis, who turned 19 last month, became the first teenager to reach the third round since Ernests Gulbis in 2008.