The shooting happened Tuesday afternoon at about 3:40 p.m. MT outside the Bank of Montreal on Crowfoot Way N.W.
Initial reports indicated a bank robbery, but police say there was no connection to the bank.
Officers were called to the area because of a suspicious vehicle, police said in a news release.
"At some point during the interaction with the occupants of the vehicle, the driver attempted to flee and mounted the nearby curb. The vehicle drove along the sidewalk, and struck two elderly pedestrians …The driver of the vehicle was challenged by uniformed members, and a service firearm was discharged."
The man the officer shot is in hospital. Two other suspects are in custody.
Stefan Danylo, who was waiting for a bus nearby, said he heard two shots. He walked over to see what was going on and spotted a man lying on the ground, covered in blood.
"He wasn't moving," said Danylo.
Police said the elderly man hit by the vehicle wasn't hurt, but the elderly woman is in hospital in serious, but stable condition.
A large area of the parking lot outside the bank was cordoned off Tuesday afternoon. Two vehicles were parked outside of the building and one had smashed windows.
The Alberta Serious Incident Response Team (ASIRT) is investigating the shooting, police said. The organization said its mandate is to conduct an independent investigation into the incident.