Tierra del Fuego judge Lilian Herraez ordered the authorities to seize boats and other assets worth $156m.
Argentina claims sovereignty of the islands, which it calls the Malvinas.
The oil companies named in the case are not based in Argentina and it is not clear how the measure will be implemented.
Drilling for oil in the territorial waters around the Falklands began in 2010 despite opposition from Buenos Aires.
Judge Herraez says the new ruling will take steps to try to seize the companies' assets abroad.
The five companies mentioned are: Premier Oil Plc, Rockhopper Exploration Plc, Falkland Oil and Gas Ltd, Noble Energy Inc and Edison International Spa.
Three of the companies are British-based, one is American, based in Texas, and one is French-owned, based in Italy.
Britain and Argentina went to war over the Falklands in 1982.
Argentina occupied the South Atlantic archipelago for 74 days, before British forces regained control.
During the conflict, 255 British and about 650 Argentine servicemen were killed, along with three Falklands civilians.
Argentina accuses Britain of colonialism, saying the islands lie some 700km (450 miles) off its coast.
Britain has held the Falklands for 180 years and says the wishes of its 3,000 residents should be respected.
The vast majority of them want the islands to remain a British overseas territory.
"They want to remain British and that view should be respected by everybody, including by Argentina," said David Cameron after a 2013 referendum in which the islanders gave almost unanimous support for the status quo.
Argentine President Cristina Fernandez de Kirchner said at the time that Britain was "arrogant" and "bordering on stupidity" for refusing to negotiate on the future of the islands.
A federal judge in Argentina has ordered the seizure of assets of five companies drilling for oil in the Falkland Islands.