The contest was halted at 7-7 in the deciding set in fading light, and will be completed Sunday, Xinhua reported.
Murray could take advantage of the delay after looking distinctly uncomfortable at times against the German 28th seed, grabbing at his left leg and requiring treatment from the trainer in the final set.
Top-ranked Rafael Nadal beat Leonardo Mayer 6-2 7-5 6-2 to reach the French Open fourth round.
The defending champion will play against Dusan Lajovic, who beat Jack Sock 6-4 7-5 6-3. The world No. 1 revealed that he had some back problem during the match.
"I felt a little bit my back, so that's why I slow down a little bit the serve," Nadal said after his 31st straight win at Roland Garros.
"I felt a little bit from the beginning. In the second match I was not serving that fast, too," he said
Nadal, who turns 28 on Tuesday, said he did not want to go into details and then tried to play it down, insisting: "I'd rather not talk about my back. You know, I've reached week No 2. I'll do my best, I'll play as best as I can, I'll put up a good fight to try and win. My back is not that important."
In the women's draw, ex-Wimbledon champion Petra Kvitova, hampered by a leg injury, lost to 2009 French Open winner Svetlana Kuznetsova 6-7 (3-7), 6-1, 9-7.
Kuznetsova next plays Lucie Safarova, who saw off Ana Ivanovic 6-3 6-3.
Fourth seed Simona Halep, the highest seed left in the women's draw, beat Maria-Teresa Torro-Flor 6-3 6-0 to set up a tie with Sloane Stephens.