The bill, aimed at thwarting British oil and gas exploration around the disputed Falkland Islands, was brought forward by Patricia Cubria, the member belonging to President Cristina Kirchner's Front for Victory coalition.
"It is a tool that continues our fight for the sovereignty and natural resources of the Malvinas [Falklands]," Ms Cubría said.
The Argentine government began legal action in June against five British exploration companies operating around the Falklands.
The ship ban follows last year's shutdown of ports by the trading bloc Mercosur (Brazil, Argentina, Paraguay and Uruguay) to ships flying the Falklands flag.
Buenos Aires province is the nation's largest and home to 40 per cent of its people as well as having its major ports, though the Port Montevideo in Uruguay is 200 kilometres away across the wide mouth of River Plate.
Last year, two Norwegian ships, thought to be British, headed to the Falklands in search of oil, docked at La Plata, close to Buenos Aires, sparking mass protests.
In December, countries belonging to South American trading bloc Mercosur closed its ports to ships flying the Falklands flag.
Two P&O cruise liners were also banned from docking in Argentina in February after they visited the islands.