The Indian Prime Minister Narendra Modi made the announcement in a television address to the nation. He said India would only be the fourth country to have used such an anti-satellite weapon after the United States, Russia and China.
Such capabilities have raised fears of the weaponisation of space and setting off a race between rival powers.
Anti-satellite weapons allow for attacks on enemy satellites - blinding them or disrupting communications - as well as providing a technology base for intercepting ballistic missiles.
India's missile was fired from a testing facility in Odisha, eastern India.
"Our scientists shot down a live satellite 300km away in space, in low-earth orbit," Modi said on Wednesday, in his first televised national address since late 2016.
"India has made an unprecedented achievement today," he said, speaking in Hindi. "India registered its name as a space power."
India has had a space programme for years, making earth imaging satellites and launch capabilities as a cheaper alternative to Western programmes.
It successfully sent a low-cost probe to Mars in 2014 and plans its first manned space mission by 2022.
The latest test was aimed at protecting Indian assets in space against foreign attacks, the government said.
"The capability achieved through the anti-satellite missile test provides credible deterrence against threats to our growing space-based assets from long range missiles, and proliferation in the types and numbers of missiles," the foreign ministry said in the statement.
The test lasted three minutes and was done in the lower atmosphere to ensure there was no debris in space and that whatever was left would "decay and fall back onto the earth within weeks", the ministry said.
Brahma Chellaney, a security expert at New Delhi's Centre of Policy Research, said the United States, Russia and China were pursuing anti-satellite (ASAT) weapons.
"Space is being turned into a battlefront, making counter-space capabilities critical. In this light, India's successful 'kill' with an ASAT weapon is significant."
China destroyed a satellite in 2007, creating the largest orbital debris cloud in history, with more than 3,000 objects, according to the Secure World Foundation.
Ajay Lele, a senior fellow at the government-funded Institute for Defence Studies and Analyses in New Delhi, said India was spurred to develop its anti-satellite capability by China's test.
US AN EARLY PIONEER
The United States performed the first anti-satellite test in 1959, when satellites themselves were rare and new.
Bold Orion, a nuclear-tipped ballistic missile repurposed to attack satellites, was launched from a bomber and passed close enough to the Explorer 6 satellite that it would have been destroyed if the nuclear warhead had been live.
The Soviet Union performed similar tests. In the 1960s and early 1970s, it tested a weapon that would be launched into orbit, approach enemy satellites and destroy them with an explosive charge, according to the Union of Concerned Scientists.
In 1985, the United States tested the ASM-135, launched from an F-15 fighter, destroying an American satellite called Solwind P78-1.
There were no tests for more than 20 years, until 2007, when China entered the anti-satellite arena.
The next year, the United States carried out Operation Burnt Frost, using a ship-launched SM-3 missile to destroy a defunct spy satellite.
Modi, who heads a Hindu nationalist-led government, has taken a strong position on national security, launching air strikes last month on a suspected militant camp in Pakistan that led to retaliatory raids by Pakistan in a dramatic ratcheting up of tension between the nuclear-armed rivals.
He faces criticism for failing to deliver on high economic growth and create jobs, but a hawkish position on security should help him at the ballot box.
The leader of the main opposition Congress party, Rahul Gandhi, congratulated the defence scientists for the programme but took a dig at Modi for making a big show of the announcement on a day that celebrates theatrics.
"I would also like to wish the PM a very happy World Theatre Day," Gandhi said.
The leader of another opposition group said it would lodge a complaint with the Election Commission against Modi for trying to reap political capital from the space programme.
India today shot down a satellite in space with an anti-satellite missile, hailing the test as a major breakthrough in its space programme.