He said that people at Digha, Mandarmoni and Shankarpur on the coast were advised to stay indoors.
Khan said a helpline would function from the state secretariat.
The MET office predicted heavy to very heavy rains at at some places over East and West Midnapore, North and South 24-Parganas, Howrah, Hooghly, Bankura, Burdwan and Purulia districts in the next 48-hours.
Kolkata would experience light to medium rainfall and an overcast sky, the MeT office said.
Fishermen were alerted and asked not to venture into the sea.
South Eastern Railway cancelled all south-bound trains beyond Kharagpur.