The targeted well is part of the Bai Hassan oil field in Kirkuk, around 250 km north of the capital Baghdad, they added. No casualties or damage was reported, reports dpa news agency.
The attack comes a day after IS claimed responsibility for an explosion at a market in Baghdad on Thursday.
The blast in the mostly Shia district of Sadr City left at least one civilian dead and 12 others injured, according to security sources. The Sunni terrorist group regards Muslim Shias as heretics.
In January, the IS claimed responsibility for a twin suicide attack that killed at least 32 people in central Baghdad, the most serious terror attack in the city in about three years.
In December 2017, Iraq declared victory over the IS, having recaptured all the territory seized by the extremists since 2014. However, members of the terror group have continued to carry out scattered attacks across the war-torn country.