Derbyshire Police said the man had been detained on suspicion of breaching Section 8 of the Iraqi Sanctions Order 2003, but had since been released on bail pending further inquiries.
Mr Ely, who recovered the 24lb piece of bronze with the help of US Marines, believes Iraqi officials decided to demand the return of the war relic after seeing media coverage of its value - placed at around £250,000.
"American Marines gave it to me and at that time Baghdad was under American control," he said.
"There wasn't even an Iraqi government and I have since turned it into a piece of war relic art. This is like having a chunk of the Berlin Wall - it's part of history but it's not cultural property."
Police have also interviewed Mr Ely about the statue and requested that he sign a document warning him that if he sold or defaced the buttock he could face prosecution.