The Manchester United captain cited criticism over his commitment to the national team as well as a desire to give younger players a chance to play for Serbia when explaining his decision to walk away.
A statement from the Serbian Football Federation read: "The Football Association of Serbia wishes to thank Nemanja Vidic for everything he has provided for Serbian football, especially playing for the national team.
"His behavior, commitment and attitude towards the national team deserves praise and a special place in the history of this sport in our country.
"While we respect his decision, we want to emphasize the door to the national team is not closed and, should all the conditions be met, it would be a great honor if he rejoined the team."
Vidic, 29, made his international debut in 2002 against Italy and went on to make 56 appearances for the national team, including a place on Serbia's team for the 2010 World Cup.