Electrical instalations and power pylons were downed by the cyclone and flights were cancelled in the region.
Tidal waves as high as three metres struck the coast and torrential rain fooded buildings.
"After landfall in coastal Andhra Pradesh, the cyclone track shows that it will move along coastal Andhra and re-emerge in the north of the bay," Ajit Tyagi, the IMD director general, said from the capital New Delhi.
Heavy rains are predicted to continue into Friday.
Armed forces have been brought in to assist with the evacuation of residents threatened by the cyclone.
Prerna Suri, Al Jazeera's correspondent in New Delhi, said: "There is extensive damage all across southern Andhra Pradesh at the moment.
"The meteorological department have been reiterating that the cyclone will be weakening, that is the good news. But the bad news is that it is just going to continue with heavy rainfall and strong winds all across the coast line.
"Neigbouring states along India's eastern coast, West Bengal and Orissa, have issued new alerts."
The Bay of Bengal region suffers regular cyclones, usually between April and November.
Cyclone Aila hit southern Bangladesh last May, killing 300 people and making about 200,000 people homeless, many of whom remain in temporary shelters.