The blasts occurred about 10 minutes apart outside a movie theater and a bus station, police officer Syed Anwarul Huda said.
The CNN-IBN television news channel said 11 people were feared dead.
Police were trying to determine the cause of the explosions, Huda said.
Television images showed the injured being taken to hospitals. The areas were cordoned off by police as panic spread among nearby people.
The last major bomb attack in India was a September 2011 blast outside the high court in New Delhi that killed 13 people.
Federal Home Secretary R.K. Singh said officials from the National Investigation Agency and commandos of the National Security Guards were leaving New Delhi for Hyderabad, the capital of Andhra Pradesh.
India has been in a state of alert since Mohammed Afzal Guru, a Kashmiri, was hanged in a New Delhi jail nearly two weeks ago. Guru had been convicted of involvement in a 2001 attack on India's Parliament that killed 14 people including five gunmen.
Many in Indian-ruled Kashmir believe Guru did not receive a fair trial, and the secrecy with which the execution was carried out fueled anger in a region where anti-India sentiment runs deep.