Police say the stabbing happened at about 6 a.m. at Bramalea City Centre, located at the corner of Peel Centre Drive and Team Canada Drive.
Police say a woman in her 20s was air-lifted to hospital suffering from multiple stab wounds. Her condition is not known.
A male in his 20s fled the scene in a car. A high-speed chase ensued, which police had to call off for safety reasons when speeds exceeded 150 kilometres an hour.
Police are looking for an East Indian man in his 20s wearing a black New York Yankees ball cap and a green shirt. Police say he has a beard and a ponytail. His is six feet tall and weighs about 200 pounds.
"There is no reason for concern to the rest of the public," said Thomas Ruttan. "These two people had a previous relationship."