Members of the group - which seized Iraq’s second city as part of its so-called Islamic State caliphate last summer - blew up a church which had been standing for thousands of years.
Conflicting reports have named the church as St Mary's and the 'Mother of Aid'.
Isis fighters inadvertently killed four children who were near the church at the time, Saeed Mamuzini, a spokesman for the Mosul arm of the Kurdistant Deomcractic Party told the Rudaw Kurdish news website.
The incident is the latest example of Isis fighters destroying ancient artefacts and monuments which either predate Islam or are aligned with un-Islamic faiths and communities, in the year that it has seized swathes of Iraq and Syria.
In the past year, Isis has released propaganda videos of militants defacing monuments in the ancient Assyrian city of Nimrud, northern Iraq before levelling the site with explosives; and using sledgehammers and Kalashnikovs to hack away at statues in the Iraqi city of Hatra.
Syria has also been targeted by the group, with the ancient city of Palmyra, the home to a set of ancient Roman ruins, falling in late May.