Hatra was founded in the days of the Parthian Empire over 2,000 years ago and is a Unesco world heritage site.
Earlier this week, IS militants began bulldozing the nearby ruins of the Assyrian city of Nimrud.
IS, which controls large areas of Iraq and Syria, says shrines and statues are “false idols” that have to be smashed.
It not yet clear how extensive any damage might have been.
Hatra, located about 110km (68 miles) south-west of Mosul, was a fortified city that withstood invasions by the Romans thanks to its thick walls reinforced by towers.
Said Mamuzini, a Kurdistan Democratic Party (KDP) local official, told Kurdish media that IS militants had started destroying the site.
“The city of Hatra is very big and many artefacts of that era were protected inside the site,” he said, adding that the militants had already taken away gold and silver.
The remains of Hatra blend Hellenistic, Roman and Eastern architectural influences
There is no independent confirmation of the destruction.
Reports of the bulldozer attack in Nimrud, an Assyrian city founded in the 13th Century BC, emerged on Thursday.
On Friday Unesco head Irina Bokova condemned the “cultural cleansing” in Iraq as a “war crime”.
“There is absolutely no political or religious justification for the destruction of humanity’s cultural heritage.”
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Last week, IS released a video apparently showing militants with sledgehammers destroying statues and other artefacts in a museum in Mosul.
In the video, the objects are described as “false idols” and their destruction defended in religious terms.
IS has controlled Mosul, Iraq’s second-largest city, and nearby areas since June 2014 – a region with nearly 1,800 of the country’s 12,000 registered archaeological sites.
The Parthian Empire was a major political and cultural force in ancient Iran. At the height of its power in the second century AD, it extended from modern-day Pakistan to Syria.
Hatra later flourished under Arab rulers, and became a major trading-post on the Silk Road across the Asian continent.