Ahead of the fixture, Man United interim head coach Ralf Rangnick confirmed that the experienced striker would be playing his final match for the club against Patrick Vieira's side.
"Out of our starting XI, there will be 10, apart from Edi Cavani, who will still be playing for this club next season," Rangnick told MUTV ahead of the contest with Palace.
Man United finished their campaign with a one-goal loss against the Eagles, with Wilfried Zaha's first-half effort deciding the fixture in the English capital.
However, the 20-time English champions still managed to claim sixth spot in the Premier League table, with seventh-placed West Ham United losing at Brighton & Hove Albion.
Cavani impressed in his first season at Old Trafford following his arrival on a free transfer, finding the back of the net on 17 occasions in 39 appearances, in addition to contributing six assists.
The 35-year-old has struggled with a number of fitness problems this term, though, managing just two goals and one assist in 20 appearances for the Red Devils.
Cavani's exit will lead to Man United entering the market to sign a new striker; Cristiano Ronaldo is set to stay despite the recent speculation, with the Portugal international only absent against Palace through injury.
Marcus Rashford was also not in the squad at Selhurst Park on Sunday amid the speculation surrounding his future at Old Trafford.
The Red Devils have finished their Premier League season with a record of 16 wins, 10 draws and 12 defeats from 38 matches, with 58 points enough for sixth position.
The 20-time English champions both scored and conceded 57, meanwhile, meaning that they end the campaign with a goal difference of zero.
In addition to Cavani, Paul Pogba, Juan Mata, Nemanja Matic and Jesse Lingard are all set to leave Man United on free transfers this summer, with the club said to be looking to wipe £80m off their annual wage bill during the upcoming market. body check tags ::