'We were afraid to go back to our house and remained in an open ground till dawn,' said a resident of Kakinada town.
Srikakulam, Vijayanagaram, Vijayawada, Rajhamundry and Tirupati towns also felt the tremors.
Immediately after the quake, authorities in the southern state alerted fishermen along the coast and advised them not to venture into the sea.
'Though no tsunami alert was issued, we still advised fishermen not to go into the sea as a precautionary measure,' said Kishore Kumar, revenue divisional officer in Kakinada.
The Hyderabad-based Indian National Centre for Ocean Information Services (INCOIS), which runs the tsunami warning system, has said that there was no need for panic as a tsunami is not likely to occur as a result of the quake.
'Usually aftershocks are recorded after a quake but there are no chances of another big earthquake,' said INCOIS director S.C. Shenoi.
Minor tremors were also felt in Kolkata, the coastal areas of West Bengal and as far inland as Jharkhand, forcing people to come out of their houses.
People made frantic calls to friends and relatives after the jolt. A few houses in the Jharkhand capital Ranchi suffered minor cracks.
In Bangladesh, Dhaka, Chittagong and Sylhet and the southern coastal region felt the quake at 2.55 a.m. local time, Star Online reported.
'The tsunami alert was issued at around 4 a.m. It was withdrawn at about 6.40 a.m.,' Meteorologist Mominul Islam told The Daily Star newspaper.