Abubakir announced in a Facebook post that "the dangerous fire on Goizha" was "brought under control at 5am, at dawn."
Mount Goizha overlooks the city of Sulaimani and is a popular spot for picnics and sightseeing.
Authorities believe the fire was sparked by a shisha pipe.
"We suspect that the source of fire could have been two to three men who had been on Mount Goizha around 2am smoking shisha. Maybe the fire got out of their control. But our investigations are ongoing," Hemin Kamar Khan, spokesperson for the Sulaimani Forestry Police, told Rudaw English.
A host of people battled to put out the fire, including "the brave teams of the civil defense police, police, Asayesh and Sulaimani Protection Brigade 1," said the governor.
Footage submitted to Rudaw by eyewitnesses appears to shows the fire driven by strong winds.
Fires are common in the Kurdistan Region's summers, when temperatures reach 50 degrees. In late July, a series of fierce fires in northern Sulaimani province raged for four days before being brought under control. The blazes damaged swathes of forests and pasturelands.
Updated at 3:02 pm
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