Cyclonic storm Baaz, which lies 400 km from Chennai, is expected to cross the coast between Chennai and Machilipatnam by Thursday night.
The Met office in Chennai said Chennai, Kancheepuram and Tiruvallur districts faced the threat of heavy rainfall and squally winds.
On Tuesday, the met office warned that 15 coastal districts, including flood-ravaged Cuddalore, Thanjavur, Nagapattinam and Tiruvarur, will experience heavy rainfall and strong winds.
But now the storm has changed its course and was moving in the west-northwest direction and only three districts in the state will face its wrath, it said.
The government machinery has been put on high alert in the three districts and fishermen have been warned against venturing into the sea.
The Met office also warned of strong winds with speeds reaching 80 and 90 kmph along the north Tamil Nadu coast.