Relief workers were using boats on Monday to ferry supplies of puffed rice and molasses to hundreds of villages cut off by the water.
"The flooding has left more than a million people stranded in the state's south," West Bengal Minister of Rural Development Surya Kanta Mishra said.
"We are reaching relief materials to them."
At least two rivers in the southern Sunderbans region had breached their banks, flooding 60 villages, officials said. Large areas of the paddy-growing state had been submerged.
They said more than a dozen people had been killed by walls collapsing in their homes and electrocution.
The unseasonal rains in largely low-lying West Bengal came after the June-September monsoon season ended in India.
Hundreds of people have already been killed in flooding and mudslides triggered by rains during the summer, which shut down India's financial hub of Mumbai for four days.
In West Bengal, thousands of people took shelter in schools and government buildings after hundreds of mud houses were washed away.
Weather officials said the rains had been triggered by a low-pressure system over the Bay of Bengal.