Mr Trump said the additional sanctions were in response to the shooting down of a US drone and "many other things".
Ayatollah Khamenei, Iran's highest authority, was singled out because he was "ultimately responsible for the hostile conduct of the regime".
Iranian Foreign Minister Javad Zarif said the Americans "despise diplomacy".
In a tweet sent after the announcement, Mr Zarif also accused the Trump administration of having a "thirst for war".
Tensions between the two countries have been escalating in recent weeks.
However, US Treasury Secretary Steve Mnuchin said Mr Trump's executive order - which would lock up "billions ...
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