The information was reported by the police in the Serbian capital.
The body of the woman, identified as Albena Dimitrova, was found in a white Mercedes SUV with Serbian license plates near the stadium of the Obilic football club.
The suspect, identified as Serbian national Raco Lazarevic, 40, is in the hospital in critical condition after trying to commit suicide.
According to Serbian media, Dimitrova was with friends, waiting for Lazarevic at a coffee shop, but left minutes before his arrival. Eyewitnesses are quoted saying they saw the man enter the SUV, shoot Albena in the head and then fire the gun at himself. He was found on the seat near the woman with severe wounds.