The ability to put satellites into orbit could indicate an advance in the Islamic Republic's missile technology, though official media gave few details.
"We need to have an active and influential presence in space," President Mahmoud Ahmadinejad said in a televised ceremony before the launch.
"Iran took its first step [to establish a presence in space] very strongly, precisely and wisely," he said. "Building and launching a satellite is a very important achievement."
State television reported the rocket had blasted off but did not show the launch. It had earlier broadcast footage of a rocket on a launch pad in desert terrain.
It said the satellite, called Omid (Hope), would be launched in the next Iranian year, which ends in March 2009.
The reported Iranian test comes in the wake of Israel's succesful launch, some three weeks ago, of a new sophisticated satellite, the TECSAR, which could boost its intelligence gathering capabilities regarding Iran.
Footage from the TESCAR was later transmitted for the first time a week after its launch.
Ahmadinejad and other senior Iranian officials were shown in an auditorium at Monday's launch, but state television did not say where it was.
Iran often announces advances in its missile technology. In November it said it had built a new missile with a range of 2,000 km, adding to the scope of its conventional arsenal.
Western experts say Iran rarely gives enough details to determine how significant its technology advances are. They say much Iranian technology is based on modifications to equipment supplied by others, including China and North Korea.
Israel and some Western powers fear Iran is covertly attempting to develop nuclear weapons. Iran insists its plans are peaceful and that it wants to generate electricity from nuclear power plants.