After a four-hour delay to the start because of the bad weather, the top seed was trailing two-time champion Kohlschreiber 3-2 in the first set when play was suspended after 23 minutes with rain setting in again.
Organisers said the match would resume on Monday at 0900 GMT.
Murray is looking to notch his first career title on the surface as he prepares for the year's second grand slam tournament, the French Open, later this month.
Bavarian Kohlschreiber, the world number 26, was a winner in Munich in 2007 and 2012 and a losing finalist two years ago.
(Reporting by Karolos Grohmann, editing by Mark Meadows)
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