"While respecting the American people and distinguishing between them and the hostile policies of the U.S. government, Iran will implement the principle of reciprocity until the offensive U.S. limitations against Iranian nationals are lifted," a Foreign Ministry statement said.
"The restrictions against travel by Muslims to America... are an open affront against the Muslim world and the Iranian nation in particular and will be known as a great gift to extremists," said the statement, carried by state media.
The U.S. ban will make it virtually impossible for relatives and friends of an estimated one million Iranian-Americans to visit the United States
Earlier on Saturday, Iranian President Hassan Rouhani said it was no time to build walls between nations and criticised steps towards cancelling world trade agreements, without naming Trump.
Trump on Wednesday ordered the construction of a U.S.-Mexican border wall, a major promise during his election campaign, as part of a package of measures to curb illegal immigration.
"Today is not the time to erect walls between nations. They have forgotten that the Berlin wall fell years ago," Rouhani said in a speech carried live on Iranian state television.
"To annul world trade accords does not help their economy and does not serve the development and blooming of the world economy," Rouhani told a tourism conference in Tehran. "This is the day for the world to get closer through trade."
The protectionist-minded Trump formally withdrew the United States from the Trans-Pacific Partnership trade deal on Monday, fulfilling a campaign pledge to end American involvement in the 2015 pact.
Rouhani, a pragmatist elected in 2013, thawed Iran's relations with world powers after years of confrontation and engineered its 2015 deal with them under which it curbed its nuclear programme in exchange for relief from sanctions.