Wing Stanojevic, together with Geraint Lewis, Danny Gray, Andy Reay, Greg Nicholls and Richard Martin-Redman, have not been offered new contracts by the Guinness Premiership title contenders.
Bristol head coach Richard Hill said: "It is never easy when you have to release players, especially when they have been at the club for quite some time and played their part in getting us to where we are today.
"But we are continually trying to move forward and upgrade at certain positions so that we can build upon what we have achieved this season.
"All the boys who are moving on are fine players in their own right and have done a good job for us when called upon.
"However, in all honesty, opportunities for them next season were going to be limited and they all need to be playing rugby on a more regular basis."