Torrential rain sparked widespread destruction, with flood water from overflowing dams submerging thousands of homes on the islands.
The affected area stretched from Flores island in eastern Indonesia to the neighbouring nation of Timor Leste.
Rescuers are still attempting to find survivors, and officials warned the death toll could rise further.
"Four sub-districts and seven villages have been impacted," Indonesian Disaster Mitigation Agency spokesperson Raditya Jati told reporters.
"After verifying the data with our team in the field, we found that there are 41 people dead. 27 people are still missing and nine people are injured."
However East Flores deputy regent Agustinus Payong Boli estimated that as many as 60 people in his municipality had died. This number has not been confirmed by Indonesian national authorities.
"The majority of them, 55, are in Lemanele village," he told AFP news agency. "Many people died here because the village was hit by both landslides and flash floods."
Officials in Timor Leste said another 11 people were killed by flooding in the capital Dili.