There are no artificial lights at French Open. The match will resume Sunday. Murray, ranked No 7, will serve on Sunday.
Murray took time outs in order to get both his upper legs massaged by a trainer during fifth-set changeovers.
At one stage, he was leading 6-5 as Kohlschreiber served, but Kohlschreiber then held a break point at 6-all that Murray erased with a backhand winner.
Kohlschreiber won the first set 6-3. Murray claimed the second and third set 6-3, 6-3. Kohlschreiber, however, bounded back winning the fourth set 6-4.
The match between Richard Gasquet and Fernando Verdasco was also suspended due to fading light. Verdasco was leading 6-3, 6-2, 2-2 when the match was called off.