The son of a key Iraqi Sunni politician and up to 50 other people have been held by security forces who say they found a car bomb in the MP's compound.
Adnan al-Dulaimi's party says his reputation is being attacked
The MP, Adnan al-Dulaimi, insists the car was not in the compound and he strongly denies any links to terrorism.
Controlled explosions were carried out after the find late on Thursday. Some reports say two car bombs were found.
Mr Dulaimi heads Iraq's main Sunni political bloc, which pulled out of the Shia-led government in August.
The American military has said that it is looking into the incident.
The MP told the BBC that up to 50 of his guards and his son Mekki had been detained since Thursday evening.
But Baghdad security spokesman Brigadier General Qassim al-Moussawi told Reuters news agency that the arrests totalled 36.
He said that the car bomb was found when security forces chased a suspected fugitive into the compound housing the MP's office.
Weapons and army and police uniforms had also been found at the MP's home, he said.
"Mr Dulaimi's bodyguards are suspected of having links to car bombs and killings," he told Reuters.
A government spokesman said the MP would be called in for questioning, and if the accusations against him were proven, his parliamentary immunity would be lifted.
The MP says he is not a sponsor of terrorism but a victim of an assassination plot.
"This is all not true. These are false accusations," Mr Dulaimi said.
"We are the ones who are subject to terrorism."
His party, the Accordance Front, said in a statement that he had been "subject to ferocious attacks to distort his reputation".
Mr Dulaimi has in the past complained against the operation of Shia militias and death squads, and strongly criticised Shia links with Iran before leaving the government earlier this year.
The BBC's Crispin Thorold in Baghdad says the incident seems certain to increase tensions between the main Sunni Arab political bloc and supporters of the Shia Prime Minister, Nouri Maliki.