A grandmother describes her "incredibly" close call with the car which crashed into Westpac Bank at Bayfair Shopping Centre this afternoon as "terrifying".

The incident, which happened around 1pm, left one pedestrian seriously injured after a person was hit by a car before it continued into the bank, according to a witness at the scene.

The grandmother, who spoke to SunLive on the condition of anonymity, was a bystander when the incident occurred.

She says she was walking with her 4-year-old granddaughter and husband, when she stepped to the side and "suddenly" the car came racing past and crashed into the bank.

"Because the car kept going after it hit the bollards, my husband immediately told us to run as we thought it was a ram raid.

"We had literally just stepped aside before the car came racing past right where we were standing moments before."

"I think if it happened one second earlier, the three of us would have been hit. It was horrible."

"We didn't even want to look back. But I saw [the car] right by my side as it happened."

The grandmother says she gave her account of what happened to police at the scene, and was told by people who had seen the security footage it was "very scary" to see how close they were.

"We gave our granddaughter a very light account of what had happened.

"We didn't want her to be traumatised."

Earlier, a police spokesperson told SunLive confirmed that they received a report of a pedestrian being hit by a car at the shopping centre around lunchtime.

"The car also collided with a building," a police spokesperson said at the time.

"Initial information is that the pedestrian has serious injuries."

"Police are investigating the cause of the crash."