Press TV, the state-run satellite broadcaster, said the animal was launched in a space capsule code named Pishgam, or Pioneer.
The development coincided with continued stalemate in the unrelated Western effort to persuade Iran to abandon its nuclear enrichment program, which Western powers maintain is designed to create nuclear weapons technology - an assertion Iran denies.
Press TV quoted the director of the Iran Space Agency, Hamid Fazeli, as saying earlier this month that "because of biological similarities between humans and monkeys, the latter were selected for the space mission."
He also forecast that Iran would send a human into space within the "next five to eight years," and said Iran would send its Sharifsat satellite into orbit before the end of March.
There was no independent corroboration of the report, which Press TV called evidence of "yet another" scientific achievement following earlier claims that satellites and living creatures had been launched into space.
Western monitors have not announced any missile launchings by Iran in recent days.
The state news agency, IRNA, said the monkey was sent into space on a Kavoshgar rocket that reached a height of 75 miles and "returned its shipment intact," Reuters reported. The monkey survived, according to Press TV.
The timing of the reported launching was unclear - either on Monday or within the past few days. An earlier attempt to launch a monkey into space in 2011 was reported to have failed.
A year earlier, Iran said it sent a mouse, a turtle and worms into space.
Western powers are sometimes skeptical of Iranian claims of technical advance, but they also fret that ballistic missiles could be used with nuclear warheads - a concern Iran has dismissed.
The news emerged as Western officials in Brussels said they had offered Iran new dates in February to resume the long-running and inconclusive nuclear talks after Iranian officials turned down a request for a meeting in Istanbul at the end of January, Reuters reported.
The idea of using animals as a precursor to human spaceflight dates to the 1950s and the space race between the United States and the Soviet Union during the Cold War.
In 1957, Moscow's scientists were the first to launch an animal - a dog called Laika - into space. The Soviet Union also won the race to send a human aloft when Yuri A. Gagarin became the first man to orbit the globe in 1961.
Spurred to respond, the United States embarked on a space program that led to the moon landing of 1969.