The 30-year-old man met the murdered man and his brother on a tram in the city, according to a police press release. The brothers were then shot by the man as they left the tram when it stopped at Komettorget.
The shootings occurred shortly after 2pm on Friday. Police report that there were several witnesses.
One of the men later died at Sahlgrenska University Hospital. The other injured man was taken to the hospital but according to police refused to register his name. The man later left the hospital on his own with the bullet still in his body.
"However he visited Östra hospital later on Friday night where he received care," hospital spokesperson Göran Samuelsson said to news agency TT.
The brothers are well known to the police.