Mohammad al-Rubai made the comment to local television network Al-Mada, saying people were making fake title deeds to unlawfully take the properties and land.
He said: "These houses belonged to Christians who fled from Baghdad, seeking refuge from violent attacks targeting them and their homes.
"The title deed documents have been falsified and the new title deeds have been lodged with the real estate registry. Many properties had been given illegally to other Iraqi citizens."
Mr al-Rubai also highlighted that the illegal land grabs could mean that if the Iraqi Christians return, two people could technically own the same property and land.
More than a million Christians - which make up two-thirds of Iraq's Christian population - left Baghdad after the US-led invasion in 2003.
An Iraqi NGO, Baghdad Our Home, has said criminals have committed more than 7000 violations against Christian properties in Baghdad since the war.
Courts in the country launched an inquiry into illegal land grabs in February.