Maj. Gen. Qassim al-Moussawi, a spokesman for Baghdad security services, says the militant was an officer in the Saudi army.
Abdullah Azam Saleh al-Qahtani is suspected of planning a "terrorist act" in South Africa during the World Cup beginning June 11, al-Moussawi said at a press conference on Monday.
He added that al-Qahtani entered Iraq in 2004 and is suspected in several attacks in the capital and elsewhere in the country.
Al-Moussawi said the 30-year-old Saudi national, who was in charge of "security" for the terror network in Baghdad, was in contact with Al Qaeda number two Ayman al-Zawahiri to "organize the plan," AFP reported.
In Johannesburg, meanwhile, South African police were reportedly investigating the alleged terror plot at the month-long tournament, the world's biggest sporting event which starts on June 11. The World Cup is expected to attract more than 370,000 foreign fans.
"The South African police are still working on getting confirmation," Nonkululeko Mbatha, spokeswoman for the national police chief, told AFP.
Despite the killing last month of Al Qaeda in Iraq's two top figures in a U.S.-assisted military operation, attacks blamed on the group have continued.
On Monday, assailants disguised in Iraqi military uniforms beheaded a Sunni cleric and stuck his head on an electricity pole in the town where he preached against Al Qaeda, the cleric's son and Iraqi police said.
The son of the cleric Abdullah Jassim Shakour told The Associated Press the gunmen wearing military uniforms came to the family house in the town of Sadiyah north of Baghdad, took his father into a room, killed him and walked away with his head.
The family found the headless body in the house, said the son, Mohammed. When they went to report the killing to the police, they saw his head on an electric pole in the center of the town.
"I was sleeping and screams from the street woke me up," said one of the victim's neighbors. "When I stepped out of my house, I saw the head of the cleric on the top of the pole."
The neighbor spoke to The Associated Press on condition of anonymity out of fear of the militants. He also said the cleric was known for speaking against Al Qaeda and called on worshippers to fight the militant group during last Friday's prayer.
A police official confirmed that four gunmen stormed the house in the morning and beheaded him. He spoke on condition of anonymity because he was not authorized to speak to the media.
The Associated Press contributed to this report.