However, diplomats say fuel imports are unlikely to be targeted because it would hurt the public not the government.
Parliament approved rationing the fuel from May 22 and the government will decide on the ration quantity and price for unrationed fuel by April 20.
Isna said: "With a positive vote of lawmakers gasoline will be rationed at a price of 1,000 rials [about 11 US cents] per litre from the start of Khordad [the Iranian month beginning May 22]."
Motorists currently pay 800 rials [about 9 US cents] a litre, making it some of the cheapest fuel in the world.
Analysts say such a heavy subsidy encourages waste, boosts smuggling to neighbouring states and is a significant drain on government coffers.
Iranian laws have to be approved by the constitutional watchdog, the Guardian Council.
Politicians also backed a proposal that the cost of subsidising fuel should not exceed 22,250 billion rials ($2.4bn), roughly the amount the government had proposed in its budget bill for the Iranian year starting on March 21.
Isna said: "The quantity of rationing and determining the proper price of unrationed gasoline will be proposed by the Management and Planning Organisation, and by the end of Farvardin (April 20) the government will pass it."
Iranian officials previously said one proposal was for private motorists to receive a ration of about 30 litres of petrol a week or 90 litres a month.