The question put to voters is: "Do you wish the Falkland Islands to retain their current political status as an Overseas Territory of the United Kingdom?" CNN reported.
Argentina and the United Kingdom have been disputing sovereignty of the islands known in Argentina as Las Malvinas, since Britons landed there in 1833.
The British government supports the referendum while the Argentinian Embassy in London said in a statement Friday that the vote had no legitimacy and was "a further attempt by the British to manipulate the question of the Malvinas Islands."
"The United Kingdom has no right to alter the legal status of these territories, not even under the guise of a hypothetical 'referendum,'" Argentina said.
Britain maintains the islanders have chosen to be British and "have a right to self-determination as enshrined in the U.N. Charter," a January statement said.
The statement added: "There are three parties to this debate, not just two as Argentina likes to pretend. The islanders can't just be written out of history. As such, there can be no negotiations on the sovereignty of the Falklands Islands unless and until such time as the islanders so wish."
Meanwhile, people living on the islands asked to choose their own sovereignty.
"The Falkland Islanders are a peaceful, hard-working and resilient people. Our society is thriving and forward-looking. All we ask is to be left in peace to choose our own future, and responsibly develop our home for our children and generations to come," the islands' government said.
Voting on the issue will continue Monday.