Peshawa Hawramani, the spokesperson for the Kurdistan Regional Government (KRG), said in a statement that the strike killed four Yemeni nationals working at the field and inflicted significant damage upon the infrastructure.
The drone strike is the first deadly attack against the Khor Mor complex owned by the United Arab Emirates firm Dana Gas, which was hit several times in recent years.
Hawramani said the attack will cause "power shortages".
"These repeated attacks must stop," Hawramani added. 
He denounced the attack as a "terrorist act" committed by "saboteurs and evil people."
Hawramani called on the federal government in Baghdad to "find the perpetrators of this terrorist act".
A drone hit the site at approximately 6.45 pm local time (1545 GMT), said Ramak Ramadan, district chief of Chamchamal where the Khor Mor complex is located.
It "targeted a fuel storage tank", he added.
The attack disrupted gas supply to the region's power plants, resulting in the loss of 2500 megawatts (MW) of electricity, the local electricity authorities said. 
Efforts are underway to repair the damage and restore the gas supply, it added in a statement. 
There was no immediate claim of responsibility.
Kurdish authorities denounced the attack and called on the federal government in Baghdad to find ways to prevent further ones.
"These attacks threaten the peace and stability of the country," regional president Nechirvan Barzani said.
According to AFP he urged the federal authorities in Baghdad to "do their duty to stop these attacks, find the perpetrators whatever their affiliation, and punish them."   
The gas field that came under attack lies between the cities of Kirkuk and Slimani, in a region administered by Kurdish authorities.
Unclaimed Katyusha rocket attacks have targeted the same complex several times in recent years without causing significant damage.
Kurdish officials have previously denounced such attacks pointing the finger at pro-Iran groups.
In January, two Katyushas targeted the gas field, causing a blaze but no casualties. This occurred during a time when some Iraqi groups were attacking military bases hosting American forces in Iraq and neighbouring Syria.
Kurdistan deputy prime minister Qubad Talabani condemned the latest attack on the Khor Mor complex.
He called on the Iraqi government and local Kurdish authorities to "swiftly launch an investigation and take serious measures to prevent the recurrence of such attacks".