The lawsuit filed with the ICJ, also known as the World Court, says the U.S. sanctions, which are damaging its already weak economy, violate terms of a little-known 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.
U.S. 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to argue that the United Nations court should not have jurisdiction in the dispute, that the friendship treaty is no longer valid and that the sanctions Washington has levied against Tehran do not violate it anyway.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.
U.S. President Donald Trump pulled out of a 2015 nuclear pact between Iran and the five permanent members of the U.N. Security Council, with his administration then announcing unilateral plans to restore sanctions against Tehran.
Under the 2015 deal, which Trump sees as flawed, Iran reined in its disputed nuclear program under U.N. monitoring and won a removal of international sanctions in return.
Although the United States' European allies have protested against Trump's move, most Western companies intend to adhere to the sanctions, preferring to lose business in Iran than be punished by the United States or barred from doing business there.
The ICJ has so far ruled that the 1955 treaty is still valid, even though it was signed long before the 1979 Islamic Revolution that triggered decades of hostile relations with Washington.