Congress MLA from Bahadurganj Tauseef Alam slipped from a makeshift wooden bridge over the river while he was on way to lay foundation stone for a school, police sources said.
Alam, who suffered hand injury, was later rescued by villagers.
The MLA from Bahadurganj in Kisanganj district has won the third consecutive term.
The makeshift Chachri bridge is the most convenient route to cross the river.