British Prime Minister David Cameron said the Trident missile system was needed because of threats from Iran and North Korea.
Sturgeon said Cameron's policies were out of touch with defensive realities.
"Trident isn't the answer to the threats we face as a country," she said in a statement. "We are pledged to get rid of Trident and only an independent Scotland will be able to do so."
Scotland is to have a referendum for independence from Great Britain on Sept. 18, 2014.
Cameron said Scotland would be better off if it decides to remain a part of the United Kingdom. Economic strength, national security and international influence were at risk of diminishing in a fractured United Kingdom, he said.
The British government has the Trident nuclear missile system deployed at its Faslane Naval Base in Scotland.
Scottish First Minister Alex Salmond said last year he would ban nuclear weapons if the country gained independence.
"Independence will allow us to take decisions appropriate to our needs, whether about defense, the economy or welfare," Sturgeon said.
McPhee, Cokas 'working on their marriage' after affair
Attkisson leaves CBS News, reportedly over network's 'liberal bias'