The Noor 3 imaging satellite was launched with support from Islamic Revolutionary Guard Corps air force specialists, Communications Minister Isa Zarepour was quoted by state outlet IRNA as saying.
It was put in orbit 450km above the Earth's surface.
The US has previously warned that successful satellite launches advance Iran's nuclear capabilities, because the process uses the same technology required to develop ballistic missiles.
Tehran, which has suffered several failed launches in recent years, has denied claims the satellites are a cover for its nuclear programme.
Authorities released footage of a rocket taking off from a mobile launcher. They did not say where the launch was carried out.
Details in the video corresponded with an IRGC base near Shahroud, 330km north-east of the capital Tehran, the Associated Press reported.
The base is in Semnan province, which is home to the Imam Khomeini Spaceport, where Iran's civilian space programme is based.
The IRGC runs its own space programme and is answerable only to Supreme Leader Ayatollah Ali Khamenei.
There was no immediate acknowledgement of the satellite launch from the West, which has previously refuted Iranian claims of successful launches.
In 2020, Washington dismissed the IRGC's first reported satellite launch as a “tumbling webcam in space” and said it would offer no intelligence.
It had previously imposed sanctions on Iran's civilian space agency and two research organisations in 2019, saying they were being used to advance Tehran's ballistic missile programme.
In 2013, Iran launched a monkey into space, which is said to have died during the flight.
In 2010, it launched a 3m research rocket into space carrying a can of worms, rats, and two turtles.