The 33-year-old former Serbia international signed a three-year contract extension in the summer of 2020 and still had one year remaining on his existing deal.
Matic joined the Red Devils from Chelsea in the summer of 2017 and has made 183 appearances in all competitions, scoring four goals.
Announcing the news on Instagram, Matic said: "After a great deal of thought, I have decided that this season will be my last with Manchester United. I have informed the board, the manager and the players of my decision.
"It has been a huge honour and a privilege to play for this great club. A big thank you to the fans for their unwavering support.
"I will now give everything until the end of the season to help my teammates finish as strongly as possible."
The former Benfica midfielder has made 26 appearances in all competitions this season.
Matic could be joined by the likes of Paul Pogba, Jesse Lingard and Juan Mata, who are all out of contract at the end of the season, in exiting the club.
Manchester United face a fight to secure Champions League qualification for next season.
The Old Trafford outfit are currently seventh in the Premier League, six points behind Tottenham Hotspurs in fourth place.
