Police said that the body had been recovered from the building in the southern German town of Bad Reichenhall on the Austrian border.
A severely injured victim was being treated at the scene and 10 slightly wounded people were recovered from the rink, the spokesman added, saying it was unclear how many casualties there had been.
The area around the rink was evacuated but 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 allow search operations in the building.