RCMP say officers tried to arrest two men in a car following the robbery, but their police car was rammed.
At that point, police say shots were fired. Both men fled in their car which crashed near Canada Way and Rosewood Street a few blocks away.
Police did not say if any of the shots that were fired came from the men involved in the robbery.
The two men fled on foot. One of them was tracked down by a police dog. Police say he was taken to hospital suffering from non-life threatening injuries. A second man was also arrested.
The Independent Investigations Office, which oversees serious police-involved incidents, has taken over the investigation.
Police are asking anyone who might have witnessed the shooting to contact the IIO.
Map: Canada Way and Edmonds, Burnaby, B.C.