Sites including Babylon, one of the world's most renowned archaeological treasures, are being damaged by the occupation forces, according to minister Mufid al-Jazairi.
The minister also said on Sunday the US-led forces needed to leave the area as soon as possible to avoid further destruction.
Heavy equipment, helicopters and other machinery used by Polish-led forces based at Babylon, 100km south of Baghdad, are causing irreparable harm, he said.
"Just their presence, with their heavy equipment, is harmful in and of itself," the minister said, adding that helicopters landing and taking off was just one of the problems.
"We don't know how much damage the military presence has caused because our experts are not permitted to enter the site.
"But we have received information that several archaeological sites have been damaged or destroyed," he said, mentioning the temples of Ninma and Nabu, and the famed palace of Nibushadnizar.
Babylon was the capital of ancient Babylonia, an early civilisation that existed from around 1800 BCE until 600 BCE.
Nebuchadrezzar II (reigned 605-562 Bc) built its most famous hanging gardens, one of the seven wonders of the ancient world.
Large parts of it were reconstructed and restored to its former glory by Iraq's former president Saddam Hussein in an attempt to restore ancient historical sites preserving Iraq's rich and diverse history.
"We already asked Bremer in June to request that an immediate end be put to these activities, but nothing happened"
Iraq's US-appointed interim Culture Minister
Describing anecdotal accounts of the damage, al-Jazairi said ancient roofs and walls had collapsed while other buildings had been destroyed or badly damaged over a period of time.
He also said workers employed by US contracting firm Kellogg, Brown & Root (KBR) had been digging and building in the area around Babylon, causing further damage.
Al-Jazairi said he did not know what the digging was for and that his department had not been informed about it.
Polish commanders and representatives of KBR were not immediately available for comment.
Iraqi officials raised the issue of damage to Babylon in June with the former US occupation governor in Iraq, Paul Bremer, and the former US-led forces commander, Lieutenant-General Ricardo Sanchez, who issued a statement saying they were aware of the complaints.
The minister said their complaints and suggestions fell on deaf ears.
"We already asked Bremer in June to request that an immediate end be put to these activities, but nothing happened," al-Jazairi said.
"We again ask the multinational forces to put an immediate end to such activities. We can't ignore any more what's going on at the site and the harm that is being done."
The Polish military contingent consists of about 8000 multinational troops operating in the southern-central region of Iraq, with many of them based around Babylon.