A suicide bomber has blown himself up inside a Baghdad mosque, killing at least 29 people including a member of parliament, during prayers in the Iraqi capital.

Police said MP Khalid al-Fahdawi was among the dead in the Sunday night attack that left 39 others wounded.

Major General Qassim al-Moussawi, a spokesman for Baghdad's military operations command, said the attack happened inside the Umm al-Qura mosque during prayers in the western Baghdad neighbourhood of Al-Jamiaah.

Al-Moussawi also raised the possibility that the bomber had inside help.

"For sure there must have been someone inside the mosque who helped the bomber. It must have been someone who is protecting the mosque," The Associated Press news agency quoted him as saying.

The blue-domed building is the largest Sunni mosque in Baghdad.

The attack hit worshippers who were praying in a special service during the Muslim fasting month of Ramadan, which is expected to end on Tuesday.

That the bomber detonated his explosives vest inside the mosque is particularly alarming, because it is reminiscent of a 2006 attack on a shrine in the city of Samarra that fuelled widespread sectarian violence and brought Iraq to the brink of civil war.

No group immediately claimed responsibility for the bombing. The mosque's security is provided by a government-supported group.