When asked if the military confirmed al-Muhajir was not in the custody of security forces, she said: "I confirm that."
Major General Abdul Karim Khalaf, spokesman for Iraq's interior ministry, had told Al-Iraqiya on Thursday that the detained man claimed he was al-Muhajir and that investigations were under way to verify his identity.
Khalaf said the man was arrested in a raid on Wednesday in the Wad Al-Hajar region of Nineveh province.
Mosul, the region's capital, is considered the last urban bastion of Al-Qaeda in Iraq, according to the US military.
US and Iraqi forces are involved in sustained military assaults targeting Al-Qaeda militants in Nineveh.
Khalaf said the arrest came after a man close to the detained individual said the Al-Qaeda chief was in a house in Wad Al-Hajar.
"The police then raided the area and captured the man who said 'I am Abu Hamza al-Muhajir,'" Khalaf said.
Al-Muhajir, whose real name, according to the military, is Abu Ayyub al-Masri, is an Egyptian national who was made the chief of the jihadist group in Iraq after a US air strike killed Abu Musab al-Zarqawi in June 2006, the US military said.
The US State Department has posted a five-million-dollar reward for information leading to al-Muhajir's arrest.