"Iranian citizens are advised to avoid non-essential travels to the US and, in case of visit, to exercise maximum caution," foreign ministry spokesman Ramin Mehmanparast said in remarks reported by the ISNA news agency.
The US is a "high risk" destination for Iranian travellers, he said citing a "targeted Iranophobia trend in the US and repeated incidents in which Iranian citizens are threatened and arrested there."
His comments came after US media reported that an Iranian citizen, Daryoush Sarreshteh, 73, died two days after being subjected to "intense questioning" by US customs on arrival November 6 at Dulles International Airport.
Mehmanparast said the interrogation was "inhumane" and demanded a "precise investigation" by US authorities into the incident.
"A five-hour unusual and inhumane interrogation of an elderly man cannot be acceptable," he said, adding that this ministry would follow up the case.
Iran and the United States have had no diplomatic relations for more than three decades. The two are also engaged in a years-long dispute over Tehran's controversial nuclear programme.
The US State Department on December 7 renewed its travel warning for Iran.