The Ministry of Defence said the building along with its famous leaning minaret was destroyed using explosives in the Iraqi city, where fighters have declared their caliphate.
Staff Lieutenant General Abdulamir Yarallah said: "Our forces were advancing toward their targets deep in the Old City and when they got to within 50 metres (yards) of the Nouri mosque.
"Daesh (IS) committed another historical crime by blowing up the Nouri mosque and the Hadba."
Isis disputed the claims, saying a US aircraft had destroyed the mosque.
The iconic 12th century mosque is one of Iraq's most famous buildings.
But since June 2014, when Isis leader Abu Bakr al-Baghdadi announced his group's caliphate, the militants' black flag had flown from the minaret.
It comes as the Iraqi army launched a renewed push, backed by Allied forces, to retake the surrounding area from the militants.
The UN says around 100,000 civilians are still holed up in the old city.
