The tropical cyclone Mahasen over Bay of Bengal is slowly moving north-eastwards towards the neighbouring Bangladesh and Mayanmar borders.
The storm centered at about 700km from Chennai will be seen moving upwards towards Mayanmar and Bangladesh in the next two days.
The atmospheric depression began last Thursday over Bay of Bengal and became a full-fledged storm on Sunday.
Since the cyclone has started moving upwards rain or thundershowers will be expected over Tamil Nadu and South Andhra Pradesh in the next two days.
"It will move initially north-northwestwards during next 12 hours and thereafter northeastwards towards Bangladesh-Myanmar coast," said a Met official bulletin.
Heavy rainfall with winds at a speed of 40-45 kmph to 60 kmph is expected to strike the islands of Andaman & Nicobar in the next 48 hours.
Thundershowers and squalls are expected in West Bengal, Bihar, Jharkhand, Odisha, Chhattisgarh, Sikkim, Assam, Meghalaya, Nagaland, Manipur, Mizoram and Tripura.
Mayanmar and Bangladesh have been put on alert ahead of the growing cyclone. Authorities in both nations issued precautionary warnings to fishermen and advised them to stay away from sea and coastal areas.
For Mayanmar, it involves a terse situation of shifting close to 140,000 internally displaced persons (IDPs) who live in tents or makeshift houses.
The IDPs are victims of religious war and have been left homeless.
"There are people still living in temporary tents. Now we are moving as many of those IDPs as we can to the stronger permanent shelters," confirmed a state government spokesperson to AFP.