Defence Ministry sources said this was the last major test that was required before the submarine could be handed over to the Indian Navy.
Mr Jaitley said in a series of tweets that the test was done by the first Scorpene class submarine Kalvari, but did not say which torpedo was tested. The sources also declined to identify the torpedo.
"Congratulations to our scientists, engineers on successfully test firing torpedo from the first indigenously built Scorpene Class Submarine.
"This indigenously built stealth Submarine Awill soon add potent underwater capability to the Indian Navy," posted Mr Jaitley.
On March 2, the Kalvari, the first of the six Scorpene submarines being built in India, had test fired an anti-ship missile for the first time.
The Scorpenes submarines are being built by Mazagaon Dockyard Limited under Project 75 with transfer of technology from the collaborator, DCNS of France. Two of the submarines are ready, and rest four are under construction.
Kalvari is undergoing sea trials and expected to be commissioned mid-2017.
The second submarine Khanderi was launched on January 12 this year, and will undergo rigorous tests and trials in the harbour and at sea, on surface and underwater till December this year, and will be commissioned in the Navy after that.
The state-of-the-art features of the Scorpenes include superior stealth and ability to launch a crippling attack on the enemy using precision guided weapons.
The attacks could be carried out with torpedoes, tube-launched anti-ship missiles both while underwater or on surface in all theatres, including the tropics, giving it invulnerability unmatched by many other submarines.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)