"#MuslimBan will be recorded in history as a great gift to extremists and their supporters," Zarif said as part of a string of tweets.
"Collective discrimination aids terrorist recruitment by deepening fault-lines exploited by extremist demagogues to swell their ranks."
Trump on Friday signed a sweeping executive order to suspend refugee arrivals and bar visas for travellers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Iran's foreign ministry had earlier released a statement saying it would reciprocate with a ban on Americans entering the country.
"Unlike the US, our decision is not retroactive. All with valid Iranian visa will be gladly welcomed," he wrote.
With more than one million Iranians living in the United States, the travel restrictions are expected to cause chaos for students, businessmen and families travelling between the two countries.
Parliament speaker Ali Larijani said the measures were proof of America's "violent racist spirit".
The foreign ministry released a travel advisory, calling on all citizens travelling to the US to "make completely sure" before leaving that they will not face obstacles.
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