The lawsuit filed with the ICJ, also known as the World Court, says the US sanctions violate terms of 1955 friendship treaty between the two countries.
The United States, which will respond formally in oral arguments on Tuesday, has yet to issue a public response, Reuters reported.
US lawyers are expected to argue that the United Nations court should not have jurisdiction in the dispute, that the friendship treaty is no longer valid and that the sanctions Washington has levied against Tehran do not violate it anyway.
The oral hearings, essentially a request by Iran for a provisional ruling, will last for four days, with a decision to follow within a month.
The ICJ is the United Nations tribunal for resolving international disputes. Its rulings are binding, but it has no power to enforce them and on rare occasions they have been ignored by some countries, including the United States.
US President Donald Trump pulled out of the 2015 nuclear deal between Tehran and world powers in May, with his administration then announcing unilateral plans to restore sanctions against Tehran.