A police spokesman in the southern German town of Bad Reichenhall on the Austrian border said it was unclear how many casualties there had been.
"We assume there were people killed," a spokeswoman for the Bavarian Red Cross said.
The area around the rink was evacuated.
Rescue efforts were complicated by continued snowfall, following a blizzard that began overnight and reportedly dumped some 30 centimeters (12 inches) of snow on the region.
The fire brigade attempted to prop up remaining sections of the roof to begin search operations in the building.