The Mujahideen-e Khalq (MEK) says 23 members and three policemen were killed in the attack on Camp Liberty, near Baghdad airport.
The MEK has been in exile since Iran's Islamic revolution in 1979. Camp Liberty came under rocket fire in February 2013 and in December 2013.
An Iraqi Shia militia, the Mukhtar Army, claimed the latest attack.
Mukhtar Army leader Wathiq al-Battat told Iran's Fars news agency that his group had frequently warned the MEK to "leave Iraqi soil as soon as possible",
The US designated the MEK (also known as People's Mujahideen Organisation of Iran, or PMOI) as a terrorist organisation in 1997 but took it off its blacklist in 2012 in view of its "public renunciation of violence".
The 23 reported deaths have not been independently verified.
US Secretary of State John Kerry confirmed in a statement that residents of the camp were killed and injured, but he did not specify how many.
He said the US would assist the UN in the relocation of all camp residents "to a permanent and safe location outside of Iraq".
The MEK sided with Saddam Hussein during Iran's war with Iraq in the 1980s but fell out with Baghdad after the Iraqi leader was overthrown by a US-led invasion in 2003.
The remaining Iranian dissidents, who advocate the removal of Iran's clerical leaders, were moved to Camp Liberty in 2012.
They have blamed Iran for instigating the attack and have called for the US and the UN to launch an inquiry.
Last year Islamic State militants fired rockets near the international airport as it sought to destabilise the capital.
A former military base in Iraq housing exiled Iranian opposition members has come under intense rocket fire.