The Serbian - who also played for Lazio, Red Star Belgrade, Real Sociedad and Olympiacos in a 19-season professional career - was approached by two men as he was getting out of his car in the affluent neighbourhood Glyfada.
One of those men fired multiple shots at Kovacevic from a Smart car, according to local reports.
The 46-year-old dived out of harm's way, suffering only superficial injuries to his wrist and knees in the process. He was taken to a local hospital for treatment.
The car was later found torched nearby, with a gun inside it believed to be the one used in the attack.
“I saw a man getting out of a car with a gun in his hand and coming towards me,” Kovacevic, who is now sports director of the Serbian Football Federation, told reporters after leaving hospital.
“I instinctively dived to the right and he fired at me. Then he ran, got into the car and disappeared.”
Athens police said it was unclear why Kovacevic was attacked, but they believe it may have been a warning without intent to actually kill.