The fourth-seeded Djokovic reached the semifinals at Roland Garros in each of the last two years, but could do little against Kohlschreiber while playing for the third time in three days.
"What is disappointing was that I couldn't find the rhythm throughout the whole match," said Djokovic, who on Friday completed a suspended three-set win from the previous round. "I was trying not to be frustrated with a lot of unforced errors. Tried to be positive and just wait for the chances."
The Serbian finished the match with 38 unforced errors, 16 more than Kohlschreiber.
Federer again started slow but got his forehand working as the match progressed.
The three-time finalist from Switzerland has lost to Rafael Nadal in each of the last three French Open finals. Federer only needs a title at Roland Garros to complete a career Grand Slam.
The Swiss star said the loss of Djokovic wasn't a big deal for him. The two were in the same side of the draw and could have met in the semifinals.
"Winning the semifinal is not winning the tournament, so it doesn't change anything," Federer said.
Roddick became only the second American to advance this far at the clay-court major since Andre Agassi in 2003, the same year Roddick won the U.S. Open. Robby Ginepri also made the fourth round in Paris last year.
"It's three matches," said Roddick, who had seven aces and only 11 unforced errors. "It's a lot better than I've done here before."
Roddick has reached at least the semifinals at the other three majors.
Besides winning the 2003 U.S. Open, he also is a two-time runner-up at Wimbledon.
But at the French Open, Roddick's best performance before this year was the third round in his 2001 debut.
"I like my chances maybe more than the other years," Roddick said. "I feel like I'm moving a little bit better on this stuff. I'm able to kind of slide into my forehand."
Fifth-seeded Juan Martin del Potro also advanced, beating Igor Andreev of Russia 6-4, 7-5, 6-4.
Information from The Associated Press was used in this report.