Feltman is to hold talks with Iranian Foreign Minister Mohammad Javad Zarif, Mehr news agency reported.
The agency did not provide any details on the visit, the first by a top UN official since Secretary General Ban Ki-moon travelled to Iran in August 2012 to attend a summit of the Non-Aligned Movement.
Iran on Sunday warned against any US military intervention in Syria, where the opposition has accused the regime of using chemical weapons last week that killed hundreds.
Iran is the main regional ally of the Syrian government which denies the accusations.
The Islamic republic also backs the powerful Lebanese Shiite movement Hezbollah, whose members have been fighting alongside Syrian regular forces for several months against a range of rebel forces out to topple the Damascus regime.
Lebanon has been hit by two deadly bombings a week apart that killed dozens, in the northern port of Tripoli and in the southern Beirut stronghold of Hezbollah.
Feltman was in Cairo last week for talks with Egyptian officials and Muslim Brotherhood leaders on how the United Nations can help facilitate reconciliation in the unrest-hit country.
The visit comes as Iran is staggering under the weight of UN and Western sanctions imposed over its contested nuclear programme.
