The airline said earlier on Twitter that flight AC624 from Toronto "exited runway upon landing at Halifax."
It did not say what caused the Airbus A320 to leave the runway after landing at Stanfield International Airport around 12:43 am (local time) today.
But heavy snow was falling in the eastern Canadian city and Environment Canada issued a snowfall alert, warning of low visibility.
The airline reported 23 people were harmed, though Halifax airport spokesman Peter Spurway said 25 people were taken to hospital with non-life threatening injuries.
Five crew and 133 passengers were on board the plane, according to Air Canada.
One passenger said they were made to wait in the snow after exiting the plane, including injured fliers.
"There was a couple people, all bloodied. Everybody was able to get out, but what was worse was that they left us for an hour outside in the blowing snow," Lianne Clark told the Canadian Broadcast Corporation.
She said some ran from the plane "because the fuel was coming out and we were scared."
Greg Wright was waiting at the airport to meet his 13-year-old son.
He told CBC News he initially thought his son was joking when he called to say there had been an accident.
"He said, 'We crashed, we crashed,'" Wright told CBC. "I was panicked."
Power was out at the airport at the time of the incident, but Spurway did not say whether the accident was linked to the accident.
"We did lose power, we're not sure if the two incidents are connected. They may be but we're not sure," he told AFP.
Spurway could not confirm reports that the plane's wings became tangled in electricity wires upon landing, saying only the Transportation Safety Board of Canada was on site to investigate the cause of the accident.
Both runways remained closed overnight, but one was scheduled to reopen in the morning.