The visit comes ahead of transition in Afghanistan, where a presidential election is due to take place in April and as US-led NATO forces prepare to leave the country by the end of 2014.
"With the transition in Afghanistan in 2014, the need for humanitarian assistance may very well increase," said the statement by the United Nations High Commissioner for Refugees.
"Iran and Pakistan, the world's two largest refugee hosting countries, will need continued international support to maintain asylum space for refugees during these difficult times."
Some five millions Afghans driven by war, oppression and poverty have crossed the border into Iran and Pakistan in the past three decades, seeking better lives and jobs.
Almost one million Afghans are illegal immigrants in Iran while some 840,000 have been able to register as refugees, according to police figures.
The UNHCR and non-governmental organisations say Afghanistan -- whose economy is mostly supported by foreign aid -- is ill-prepared to host a large return of refugees after the departure of NATO forces.
Iran is also facing its own economic hardships, exacerbated by international sanctions over its disputed nuclear drive that have crippled its economy.
During his two days visit, "will meet Iranian officials and international missions stressing the commitment of UNHCR to support the Government of Iran," said the statement.
A UN source said Guterres was also likely to discuss with Iranian officials the Syrian conflict and the plight of millions of people who have fled the nearly three-year war.
Iran is a staunch supporter of Syrian President Bashar al-Assad's regime, which has been battling rebels trying to topple his government. The conflict has killed more than 140,000 people.