The executive order also stops the admission of all refugees to the United States for four months.
No formal relations
The United States and Iran have not had formal diplomatic relations since April 1980, when President Jimmy Carter cut ties during the Iran hostage crisis. American interests in Iran are represented by the Swiss Embassy in Tehran.
The US State Department has warned Americans for years about the risks of traveling to Iran.
The most recent travel warning, updated on the department's website in August 2016, says Iran unjustly imprisons US citizens, especially Iranian-Americans, on charges of espionage and being a threat to national security.
Another source of friction between the United States and Iran is the future of the nuclear deal negotiated during former President Barack Obama's administration.
Trump said during the campaign that he would renegotiate the deal, but Iranian President Hassan Rouhani has said that won't happen. "Do you think we and our nation will let him do that?" Rouhani said.
Clarification: An earlier version of this article suggested that Americans would be banned from entering Iran. The Foreign Ministry statement says Iran has not yet decided on specific actions, but that it would consider legal, political and retaliatory measures against President Trump's executive order.
By CNN