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.

The medicine does not contain the ingredient that produces the high associated with recreational cannabis.
The treatment, called Epidiolex, is based on one of the non-psychoactive components of the cannabis plant, CBD.
Early studies in the US have shown treatment with CBD may reduce the frequency and severity of seizures in children with severe forms of epilepsy.
The new trial marks the first time the treatment has been tested in the UK.
Patients are being enrolled for a trial of the treatment at Edinburgh University's Muir Maxwell Epilepsy Centre, based at the Royal Hospital for Sick Children in Edinburgh, and Great Ormond Street Hospital.
The Royal Hospital for Sick Children in Glasgow and Alder Hey Children's Hospital in Liverpool are also driving the study.
There are further centres in the US, France and Poland.
Their initial focus will be on children with Dravet Syndrome, a rare but serious type of epilepsy that is difficult to treat. Some children will receive the treatment while others will receive a placebo.
In a further phase, researchers will also study the effect on children with Lennox-Gastaut Syndrome.
Only children whose seizures cannot be controlled with existing medications will take part in the trial.
Dravet Syndrome usually takes hold in the first year of life. It causes seizures that are often prolonged, lasting longer than five minutes.
They then develop other seizure types. This has a significant impact on the child's development and can be fatal in some cases.
Epidiolex has been developed by the British biotechnology company GW Pharmaceuticals, which is sponsoring and funding the trial.
Dr Richard Chin, director of the Muir Maxwell Epilepsy Centre, said: "Many children with serious forms of epilepsy do not respond to the medications that we currently have available.
"We need new means of treating these conditions so that we can give back some quality of life to these children and their families."
A federal judge in Argentina has ordered the seizure of assets of five companies drilling for oil in the Falkland Islands.
[NEXT_CONCEPT]
Children with severe epilepsy could be helped by a new treatment derived from the cannabis plant.