The white bus overturned in a residential area in the coastal town of Canico, its mayor, Filipe Sousa, told reporters. TV images showed the vehicle on its side on a bank next to a narrow road and surrounded by rescuers.
Other members of the same group of German tourists were travelling in another bus, which was not involved in the accident, a regional civil protection spokesman told a news conference.
Portuguese President Marcelo Rebelo de Sousa told SIC TV that some of the victims were from Madeira but most were German.
Madeira is a popular tourist destination. The peak season is during the summer but it also gets many visitors during Easter.
Portuguese Prime Minister Antonio Costa sent a message of condolences to German Chancellor Angela Merkel.
(Production: Silvio Castellanos, Catherine Macdonald)