With their faces hooded, the two men struck at a Swedbank office in Gränby Centrum just before 9 a.m.
Security guards had delivered money to the bank and emptied a night safe when they were apprehended and forced into a small room by the armed attackers. There they were held at gunpoint until they handed over an undisclosed sum of money.
One of the men then fled on foot while the other made his getaway on a bicycle.
A man who had witnessed the robbery drove after the two masked raiders in his car. At least one shot was fired at the car but failed to hit its target.
Police were close to capturing the men at one point but later lost track of them.
“We are checking several addresses where the men could be, but we haven’t found them yet,” police spokesman Christer Nordström told news agency TT.