Heavy equipment, helicopters and other machinery used by Polish-led forces based at Babylon, 100 km (60 miles) south of Baghdad, are causing irreparable harm, Mofeed al-Jazaeri said.
"Just their presence, with their heavy equipment, is harmful in and of itself," the minister told Reuters, saying that helicopters landing and taking off were a particular problem.
"We don't know how much damage the military presence has done because our experts are not permitted to enter the site.
"But we have received information that damage has been done to several archaeological sites," he said, mentioning the temples of Nenma and Naboo, and the famed palace of Nebuchadnezzar.
Babylon was the capital of ancient Babylonia, an early civilisation that existed from around 1,800 BC until 600 BC.
Most famous for the hanging gardens built by Nebuchadnezzar, one of the seven wonders of the ancient world, large parts of it were reconstructed by Saddam Husssein in an attempt to associate himself with his country's former glories.
Describing anecdotal accounts of the damage, Jazaeri said ancient roofs and walls had collapsed and buildings had decayed.
He also said that workers employed by US contracting firm Kellogg, Brown & Root (KBR) had been digging and building in the area around Babylon, causing further damage. Jazaeri said he didn't know what the digging was for.
Polish commanders and representatives of KBR were not immediately available for comment.