While three of them were rescued, two girls identified as Pinki Kumari (14) and Dhanmanti Kumari (10) are missing, they said.
The incident occurred at Doman Bigha village in Hilsa sub-division of the district. The girls had gone in a religious procession to immerse the idols of Shiva-Parvati at the end of 'Teej' fast.
"The girls stepped into the river, which is currently in spate after heavy rains, near Sohara bridge. They lost their footing and swept away immediately," Deputy Superintendent of Police Parvinder Bharti said.
The district administration has launched a search operation for the two missing girls with the help of divers, the DSP added.