A police spokesman said officers were called to the corner of Frederick St and Anzac Ave about 7.20pm on Friday, shortly after the finish of the Fifa Women's World Cup match between Switzerland and the Philippines.
"It appears one person received minor injuries and was transported to hospital," he said.
A witness at the scene said the driver was attempting to make a left turn from Anzac Ave into Frederick St while large numbers of people were crossing on the green pedestrian signal.
"The driver seemed frustrated at the presence of the amount of pedestrians and not being able to proceed and was gesticulating — arms waving.
"The driver then proceeded to nudge through the line of pedestrians — myself included — without any regard to anyone else’s safety.
"They then briefly stopped in the middle of the pedestrian crossing area before accelerating away and knocking over and injuring two pedestrians in the process.
"The actions of this driver were absolutely disgraceful."
A police spokesman said the driver had not been charged at this stage, but inquiries were ongoing.
He reminded drivers to be particularly vigilant at the moment, because the World Cup had brought a major increase in foot traffic to the city.
"Be aware of your surroundings, drive to the conditions and stay alert.
"Don’t drive under the influence, or distracted, and always wear a seatbelt.
"The speed limit is just that — a limit, not a target."
