Police said the boat with about 19 pilgrims and oarsmen were on way from Sukhchar in North 24 Parganas district to here when it capsized near the Baro Madirtala ghat.
The pilgrims were bound for Shakuntala Kalibari at Konnagar in Hooghly district.
Locals immediately jumped into the river and rescued 12 pilgrims, the police said.
Efforts are on by the district administration and the police to trace the missing, the police added.