According to sources, the test was conducted on March 31 from Arihant in the Bay of Bengal. The missile was fired from around 20 metres under water, and covered a distance of 700 km before hitting the target.
Prior to that, a dummy was also test-fired from a pontoon on March 7, the sources said.
Both the missile and the submarine have been developed by the Defence Research and Development Organisation (DRDO).
Arihant, the lead ship of India's Arihant-class of nuclear-powered ballistic missile submarines, has been designed based on the Russian Akula-1 class submarines.
The DRDO was, however, tight-lipped over the test.
The K-4 is part of the K-family of missiles, a series of submarine-launched ballistic missiles (SLBM), named after former president and scientist A.P.J. Abdul Kalam.
The missile was developed specifically for Arihant, as the nuclear capable Agni-III could not be compacted to fit in the submarine. Arihant has a 17 metre diameter hull.