The Uruguay striker, 35, played for only the fifth time in 2022 as the Red Devils' season ended with a 1-0 defeat at Crystal Palace.
Before the match, interim manager Ralf Rangnick confirmed Cavani would leave United when his contract expires on June 30.
A video has emerged of the striker pointing at a supporter and gesturing with his middle finger before boarding the team bus outside Selhurst Park.
It remains unclear what was said to provoke Cavani and whether the finger was aimed at a United or a Palace fan.
The Uruguayan leaves Old Trafford after a mixed two-year spell, netting 19 goals in 59 appearances.
After an influential debut season, a combination of injury and the arrival of Cristiano Ronaldo saw his game-time drop during the 2021/22 campaign.
And Cavani recently admitted he would've tried to leave United last summer if the signing of Ronaldo was confirmed sooner.
"At the moment it was done, I thought it was a good thing for Manchester to sign Cristiano," he told ESPN Brasil.
"Knowing a bit about the world of football these days, the first thing I did was call my [brother and manager Walter Fernando Guglielmone] and said, 'Fernando, if this had happened a week ago, I would ask you to find me another club'.
"But not because I didn't want to play with Cristiano Ronaldo. No. Because I had the opportunity to know him, and he is a great professional, with his targets, and that is perfect for a sportsman. But as I know, after years in football, how things work these days. That's why I spoke to my brother."
Cavani added: "My way of thinking and seeing football showed me that I was right in the first few months and on… I had my problems with injuries and I've been away for a while. But that was a bit of what happened in that stretch."