There was no immediate information on damages or casualties in Israel or elsewhere.
The quake's epicentre was in Penjwin in the north-western Sulaimaniyah province within the semi-autonomous Kurdistan region very close to the Iranian border, according to an Iraqi meteorology official.
A 7.2 quake struck near the Iran-Iraq border on Sunday, the United States Geological Survey said.
At least four dead were also reported in Iraq's Kurdistan region.
Iran's state TV reported that at least eight villages were damaged in the natural disaster.
The temblor, centered about 350 kilometers (217 miles) north of Baghdad, was felt throughout Iraq, USGS said. At least eight villages have been damaged.
The quake struck the mountainous area of Sulaimaniyah province at around 9.18 pm (6.18pm GMT) at a depth of 21 miles, the monitor said.
But governor of Qasr-e Shirin Faramarz Akbari said only two people had died in the town and 25 others were injured. "Electricity has been cut in some villages and rescue teams have been dispatched to those areas", the report said.
It was so strong that it was felt in various cities in Western Iran and even Tehran, and also in the neighbouring countries, particularly Kuwait.
Witnesses reported on social media that they felt the shocks as far as Baghdad and Mosul.