The city says the fire, which happened in a manhole Saturday night, "completely destroyed the electrical infrastructure" inside.
Over 100 buildings, including apartments and office towers are affected.
Nenshi and other officials told a news conference that it could be Wednesday at the earliest before power can be restored, and the wait could be as long as Saturday for others.
The mayor says employers in the affected area should tell their employees not to come in on Tuesday.
He says the city will assess whether to advise other workers outside the affected area to also avoid coming to work downtown when the work week resumes after the Thanksgiving break.
"It will not be possible. It will not be possible early this week for there to be business as usual in those affected areas," Nenshi said.
"There will be major disruptions to the affected area until the infrastructure is rebuilt."
Nenshi noted that if employees needed to get into offices to pick up files or laptops, it should be arranged outside of rush hour.
A spokeswoman for Enmax said more than just repairs were needed — the damaged equipment needed to be rebuilt.
The cause of the fire is still under investigation.
Police had set up a security perimeter around part of the affected area, but Nenshi said it was now down to just the block where the fire occurred.
Approximately 2,100 businesses and 5,000 residents are affected.
Matt, a cook at Lord Nelson's Bar and Grill which is just outside the affected zone, said his 16th floor apartment has no power.
"I feel like, what the heck? I feel upset. This is Canada, it's not in Africa. Why is it four to seven days before the hydro can be back?"
He said emergency workers and roadblocks were everywhere when he left work Saturday night, and that it looked like an action movie. When he finally reached his building, he had to wait half-an-hour before security guards would let residents enter.
He took the stairs because there was no power to run the elevators. There was still no power when he got up Sunday morning, and the water for his shower was starting to get cold.
"It's Thanksgiving and a lot of people won't be able to cook their turkeys," he said.
Alberta Justice tweeted that it was still assessing how services would be affected at its courthouse, which is in the zone without power.
The province's emergency alert system was also activated to warn people that 9-1-1 phone service in Calgary's downtown core may be disrupted due to the power failure.
The city says some upper floors in buildings may also lose water pressure due to the outage. It said it was preparing to provide emergency potable water wagons for affected residents and businesses.
An emergency information centre has also been set up where they will be food trucks, hand washing stations and places for people to charge electronic devices.
It's the second major power outage to hit Calgary in about a month.
About 30,000 people lost power in September when a series of heavy snowfalls hit the city and snapped tree limbs that pulled down power lines.
Nenshi warned against things like running vehicles in underground parkades because the ventilation systems in the garages weren't working. He said people also should unplug everything to prevent a surge for when power eventually returns.
"It's also a good time to contact your insurance company."
This is underground electrical fire in downtown #yyc Saturday night. Many without power.October 12, 2014
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