However, officials have reported his arrest or killing before, only to later say they were wrong.
Major-General Qassim al-Moussawi, a military spokesman, said the government
was certain the man arrested was al-Baghdadi and showed what he said was the first known picture of him.
The US military said it was working to verify who was captured.
Al-Baghdadi is the purported head of the Islamic State of Iraq, one of a handful of Sunni Arab groups accused of attacks in the northern city of Mosul and other parts of Iraq.
The US has previously said al-Baghdadi could be a fictitious character, used to give an Iraqi face to an organisation dominated by foreign al-Qaeda fighters.
A security official said information from al-Baghdadi had led Iraqi authorities to arrest four people plotting an attack to coincide with the birthday of Saddam Hussein, the former president who was toppled by US forces in 2003.
|Some Iraqis continue to mark the deceased
former leader's birthday [AFP]
Saddam was hanged in December 2006 after being convicted of crimes against humanity by an Iraqi court.
He would have turned 72 on Tuesday.
Some Iraqis marked Saddam's birthday in his native town of Awja, near Tikrit, by reading poems and verses from the Quran.
"We will not forget Saddam Hussein, that we lived under his protection for decades," one 40-year-old mother was quoted by the AFP news agency as saying.
"We will raise our kids on his love and visit his grave on all occasions. The birthday of the late president is precious to our hearts and always will be."
Relatives and supporters in Awja laid wreaths by his grave and chanted slogans against George Bush, the former US president, who ordered the US-led invasion that ended Saddam's rule.