Both people injured were inside the building at the time.
A Fire and Emergency spokesperson said there had also been a multitude of calls following the tornado, with reports of roofs being torn off and air conditioning units falling off buildings.
Canterbury Weather Updates tweeted that there were reports of "minor damage and more sightings".
"It has literally picked up a truck and moved it across the yard," he said.
"Those yellow bins were flying round the yard in a tornado-like thing. It's passed over now. Bloody hell. Terrible experience," his mum said.
Alison Kendall of Richmond Discount Furniture near Linwood College in East Christchurch said the tornado blew a Toyota Hiace fruit and vegetable truck outside her shop into a fence about 20 metres away.
"It was horrific. I don't know how much damage it's doing as it goes around the area," she said.
She said she ran to shut the large main door of her shop when she heard hail, but tripped and fell sideways at the door.
"Next minute I'm hearing the windows smashing," she said. "I jumped back again and came over to where the windows smashed. You could see that the tornado sucked them out, it didn't blow anything into them. It was like a huge dust storm, I've never experienced anything like it."
She said the fruit and vegetable shop next door had a lot of produce containers stacked outside and they were "flying everywhere".
"He had his truck parked outside. That ended up over by the fence 20 metres away," she said.
"I had a lady pull up in her car and said, 'Can I come in to take shelter?' She was terrified and said there were pieces of roof flying off in Fitzgerald Ave."
Christchurch Weather Updates director Russell Voice said there were at least two separate tornadoes in the storm - one that hit the central city, apparently including Sydenham and Linwood, and a water spout at sea. Both have now dissipated.
"There was a small tornado near the CBD that has caused quite significant damage over a very small area. It was quite isolated," he said.
"There could be a few more thundery hailstorms and strong winds, but the likelihood of any more tornadoes is pretty low now because it's starting to cool down."
Orion Energy spokeswoman Linda McGregor said the tornado had cut power to a small number of properties in the Waltham area. "We are assessing the damage, but it is potentially less than 10 single premises," she said.
The tornado hit about the same time as hail rained down on the city.
MetService said a Severe Thunderstorm Warning has since been lifted for the Canterbury radar area.
Meanwhile, a house has been hit by lightning near Palmerston, Otago, this afternoon as wild weather hit large parts of the South Island.
A Fire and Emergency New Zealand spokesman said it received a call at 1.10pm reporting a lightning strike on Palmerston-Hampden Rd in the Waitaki District town 50km north of Dunedin.