“Horrible news come to us from Madeira," a German government spokesman tweeted after the deadly crash.
"Our deep sorrow goes to all those who lost their lives in the bus accident, our thoughts are with the injured," he added.
The German embassy in Lisbon confirmed to AFP that a number of its nationals were among the dead, without giving any figures.
Filipe Sousa, mayor of Santa Cruz where the accident happened, said 17 women and 11 men were killed in the crash, with another 21 injured,. The regional protection service in Madeira did not confirm those figures.
"We only know that there were German victims, For the moment we don't know either the names or the number of the victims," an embassy spokesman said.
Portuguese Prime Minister Antonio Costa said on Twitter that he had contacted German Chancellor Angela to convey his condolences.
"It is with profound sadness that I heard of the accident on Madeira," he wrote on the government's Twitter page.
"I took the occasion to convey my sadness to Chancellor Angela Merkel at this difficult time," he added.
Televised images showed the bus had spun off the road, apparently having flipped several times, before crashing into a house at the bottom of a slope.
The deadly accident took place at 6:30 pm (1730 GMT) and left another 21 people injured, according to the Santa Cruz mayor.
Portugal's President Marcelo Rebelo de Sousa said he would travel to Madeira overnight.
Medical teams were sent to the scene of the crash to carry out autopsies on the dead.
Often called the Pearl of the Atlantic, Madeira hosts thousands of tourists each year, attracted to its subtropical climate and rugged volcanic terrain.