UF's first couple is part of a delegation that includes six US university presidents. Other universities represented include Cornell University and the University of California, Davis.
The purpose of the trip, organized by the Association of American Universities, UF's peer group, is to foster scientific and academic exchange between the US and Iran, said AAU spokesman Barry Toiv.
The presidents were invited to Iran by the president of Sharif University of Technology in Tehran, which is hosting the visit, he said.
While in Iran, the presidents will visit universities in Tehran and elsewhere and meet with their presidents and faculty, he said.
At Sharif University, the presidents will also be part of a forum with Iranian students, he said.
UF spokesman Steve Orlando said Machen would return Thursday or Friday.
The Richard Lounsbery Foundation will pay for most of the group's travel expenses, Toiv said.
Paul D'Anieri, dean of the College of Liberal Arts and Sciences, said he thinks the trip may help improve relations between the US and Iran.
An academic delegation will be able to build contacts without politics getting in the way, D'Anieri said.
During the Cold War, he said, academic relationships between the US and the Soviet Union laid the groundwork for a friendlier relationship between the countries. The exposure to different ideas also helped people in the Soviet Union realize they wanted to change their society, he said.
The fact that Machen was one of six university presidents to be chosen for the trip is a sign of UF's prominence in international affairs, he said.