The Civil Protection authority on Friday morning located the missing tourists.
They had fled to a cave in a mountainous part of Porto Moniz and an operation to rescue them from the area was under way, it said on social media.
"It was a complicated night, a difficult night," Civil Protection secretary of state Patricia Gaspar told public broadcaster RTP at Lisbon's military airport.
A few houses have been destroyed in Calheta and Porto Moniz, but no serious injuries reported so far, authorities said.
Porto Moniz mayor Emanuel Camara told RTP it was a "night to forget" and that "many people" were evacuated as a precaution.
Persons:
Catarina Demony, Porto, Porto Moniz, Patricia Gaspar, Carlos Teles, Emanuel Camara, Gaspar, Inti Landauro, John Stonestreet
Organizations:
Friday, Porto Moniz, RTP, Camara de Lobos
Locations:
Catarina Demony LISBON, Portugal, Madeira, Calheta, Porto, Camara, Funchal