There would be no take-offs or landings from the usual opening of the airport at 6:00 am local time (0500 GMT) to noon on Tuesday, the transport hub announced late on Monday.
"The reason for this is the forecast freezing rain in the night from Monday to Tuesday, which is expected to make safe flight operations impossible in the morning," the airport said in a statement.
Ground staff at Germany's second-largest airport would use the morning to de-ice the tarmac.
"However, it can be assumed that the majority of flights will also have to be cancelled during the rest of the day for safety reasons," the airport said.
The airport advised passengers to contact their airline before travelling.
Munich airport closed already on Saturday as snow swept the south of Germany, paralysing rail traffic in the Bavarian capital and other parts of the region.
Train traffic had resumed by Monday, although the cold weather was still causing disruption to suburban rail services in Munich, according to local media.
Service at the city's main train station remained "very limited" on Monday, according to national rail operator Deutsche Bahn, with only a few long-distance trains arriving or departing.
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