Cyclone Gamane was projected to skim the island that sits in the Indian Ocean east of southern Africa but changed course and made landfall in the north on Wednesday, the BNGRC national disaster management office said on Thursday morning.
Six people have drowned, and five others were killed by collapsing houses or falling trees, authorities said.
Some 7,000 people on the island were affected by the storm, according to Madagascan authorities.
The cyclone moved slowly, amplifying its destructive effects. Video images showed torrents of water rushing through villages and people making human chains in waist-deep water trying to help those trapped in their houses escape the deluge. Numerous routes and bridges were flooded and cut off.
"It's rare to have a cyclone like this. Its movement is nearly stationary," General Elack Andriakaja, director general of the BNRGC, said, adding, "when the system stops in one place, it devastates all the infrastructure. And that has serious consequences for the population. And significant flooding."
Andriakaja said the low-pressure system was expected to "graze the northeast coast of Madagascar but it is a natural phenomenon and there was a change in trajectory."
The general also said Gamane "finally came to hit the Vohemar district" at 5:45 am on Wednesday.
Gamane has been re-classified as a tropical storm and was expected to leave the island on Friday afternoon, according to meteorologists.
Cyclone season in southwestern Indian Ocean normally lasts from November to April and sees around a dozen storms each year.