The floods swept away 17 houses on Flores, an island 1,030 miles east of the capital of Jakarta, said Paulinus Domi, head of the local district of Ende.
Police said they were searching late Tuesday for the missing in Ende.
The mudslides also damaged bridges, cut off phone lines to remote villages and forced authorities to close the local airport.
No other details were immediately available.
Flooding and landslides have killed more than 100 people on several Indonesian islands since the current rainy season began in late November. Many of the disasters have been blamed on deforestation caused by rampant illegal logging.