Hector Timerman demanded that the British confirm the location of nuclear submarines in the region.
But UK officials said the accusations of militarisation were “absurd”.
UN chief Ban Ki-moon earlier called on both sides to avoid an “escalation” in tensions over the Falkland Islands.
The two countries went to war in 1982 over the British overseas territory.
Mr Timerman told a news conference at the UN in New York that the UK was “militarising the region”, repeating accusations made by Argentine President Cristina Fernandez de Kirchner earlier this week.
“Argentina has information that, within the framework of the recent British deployment in the Falklands, they sent a nuclear submarine with the capacity to transport nuclear weapons to the South Atlantic,” Mr Timerman said.
He did not elaborate on the information, but said the vessel was Vanguard-class, a group that carries Trident nuclear missiles.
He added that Mr Ban had agreed to talk to the British about Argentina’s complaints.
The Latin America and the Caribbean region is designated a nuclear-free zone under a treaty signed in the 1960s.
In response, Britain’s UN envoy Mark Lyall Grant said the government does not comment on the “disposition of nuclear weapons, submarines etc”.
And he dismissed the accusation that the UK was militarising the situation as “manifestly absurd”.
“Before 1982 there was a minimal defence presence in the Falkland Islands,” he said.
“It is only because Argentina illegally invaded the Falkland Islands in 1982 that we had to increase our defence posture. Nothing has changed in that defence posture in recent months or recent years.”
The UK had earlier said it was carrying out routine operations in the South Atlantic, which includes the deployment of one of its most advanced destroyers, HMS Dauntless.
Prince William, the grandson of Queen Elizabeth II and second in line to the throne, has also been sent to the islands for a tour of duty in his job as a helicopter rescue pilot.
The BBC’s Barbara Plett at the UN in New York says the dispute is raised every year at the UN, and usually involves both sides sending letters to the secretary general.
But this year is the first time Argentina has provided such a detailed and public account of its grievances, she says.
It is not clear if Argentina plans to pursue any further action at the UN beyond the current protest.
The UN General Assembly has already passed non-binding resolutions urging the two to solve the dispute through negotiations.
The UK says the islanders have the right to self-determination, and London will enter into negotiations on the status of the Falklands only if the islanders request it.
The status of the islands, known in Argentina as the Malvinas, is still a highly sensitive issue for Buenos Aires.
In recent months, the Argentine government has stepped up its rhetoric on the issue and has sought support among its South American neighbours.
In December, regional trading bloc Mercosur closed its ports to ships flying the Falkland Islands flag.