The incremental costs are "entirely reasonable" for a mission that's "having a meaningful impact against this genocidal terrorist organization, the so-called 'Islamic State,'" Kenney said in a statement Monday.
"We just saw this savage organization behead 21 people for the crime of being Christian in Libya this week, [and] burn a Jordanian air force pilot alive last week," he said.
The government's cost estimate, long sought by the opposition, comes one day before parliamentary budget officer Jean-Denis Frechette releases his own calculations Tuesday morning.
Before Monday, the government had declined to reveal the expected cost of the mission. Both the New Democrats and Liberals have complained that other countries, such as Australia and the United States, were quick to release cost estimates for their missions against ISIS.
The $122 million estimate for Canada is for a six-month mission that began last October and goes until the end of the fiscal year on March 31, James Bezan, parliamentary secretary to the defence minister, told CBC's Power & Politics.
Bezan said the money is going for such things as munitions, troop deployment and other expenses "above and beyond the normal costs of operating the Canadian Armed Forces."
The final cost of the mission is expected to be higher than $122 million, Kenney said.
"Obviously, if we decide to bring our troops back or extend the mission, there would be additional costs and we would seek further approval from Parliament," he said.
Canadian CF-18s based in Kuwait began taking part in airstrikes against ISIS targets in Iraq last November. Canada's military has also deployed special forces to train Kurdish Peshmerga forces in northern Iraq.
Capt. Paul Forget from the Royal Canadian Navy and Canadian Joint Operations Command recently said the military has planned for a possible extension of the mission, but added that plans for personnel and equipment to return to Canada are also in place.