The Agni-III missile was launched from Wheeler Island, 180km northeast of Bhubaneshwar in the eastern state of Orissa, defence officials said on condition of anonymity.
In May, Pranab Mukherjee, the Indian defence minister, said that the Agni-III, India's longest-range ballistic missile, was ready but that the country was observing "self-imposed restraint" before testing.
Opposition parties criticised the announcement, saying testing was delayed because of pressure from the United States. New Delhi and Washington reached a deal in March that will lift sanctions on India's access to civilian nuclear technology.
The test launch comes four days after North Korea sparked an international outcry by test-firing seven missiles.
A Defence Research and Development Organisation (DRDO) source said the Indian test was "successful."
He said scientists had detected a snag in the booster rocket system of the Agni-III two weeks ago and had delayed its test. "Now we have papered over the problem and hence the launch window was chosen as Sunday," he said.
The missile was tracked during take-off, re-entry into the Earth's atmosphere and splashdown in the Bay of Bengal, another defence official said.
The Agni (Fire) is one of five missiles being developed by the DRDO under its integrated guided missile development programme launched in 1983. The others are the Prithvi, the surface-to-air Trishul (Trident), multi-purpose Akash (Sky) and the anti-tank Nag (Cobra).