"According to information we have received, 24 people have died. We are awaiting further data from people on the ground," Widada, from the disaster coordinating agency in the provincial capital Surabaya told AFP.
Heavy rains have inundated the area since Saturday, he added.
The state-run Antara news agency said hundreds of houses in four villages in Jember district had been washed away by the floods after the swollen Kaliputih river burst its banks.
"Many victims have not been found. Many of them may have been buried in the mud," local police chief Soejatmiarto was quoted as saying.
Severe flooding, much of it blamed on rampant deforestation and the development of natural water catchment areas, is not unusual during Indonesia's rainy season.