The Toffees secured their Premier League survival after they completed a stunning comeback from 2-0 down at half-time to win 3-2 against Palace, thanks to a late Dominic Calvert-Lewin header.
Fans came onto the field following the England forward's priceless goal, before igniting a full-on pitch invasion at the full-time whistle. Footage has since emerged of Vieira walking through thousands of Everton supporters when someone goaded the Crystal Palace manager by making gestures in his face. It is unclear whether the individual said anything to Vieria.
The former tough-tackling French international then retaliated by kicking the supporter before grappling with him and getting himself into a confrontation with multiple Everton fans.
The Crystal Palace boss was eventually led away by others, but will surely be expecting a phone call from the FA in the coming days to explain his actions on the Merseyside pitch.
"People would say don't react, but I disagree. If someone is in your face, what do you do? Having fans on the pitch is not the way forward, we have to stop letting fans on the pitch. You can't have players in fear of their lives if players are on the pitch. For any players or member of staff on the pitch, it's a scary place to be."
Ugly scenes between Everton fans and Crystal Palace boss cap off grim week for supporter behaviour at football grounds
The incident between Vieira and Toffees fans comes just days after the shocking incident at the City ground, where Nottingham Forest fans stormed the pitch following their Championship play-off semi-final victory over Sheffield United.
During the celebrations, Blades forward Billy Sharp, who was standing and watching on the touchline, was headbutted by a Forest supporter in a completely unprovoked attack. Sharp required stitches and was knocked to the ground.
According to BBC News, 30-year-old Reds supporter Robert Biggs pleaded guilty to assault occasioning actual bodily harm and was jailed for 24 weeks.
Following the sickening incident, Sharp's manager Paul Heckinbottom was quoted by Yorkshire Live as saying:
"If you watch every Monday night football, Sunday or whatever there are always things thrown on the pitch, fan invasion and commentators and ex-players all say the same thing about the safety of the players and nothing has ever been done.
"Bill's minding his own business off the pitch, trying to get our players away and he's assaulted on the blindside, cowardly. He was knocked to the ground, stitches, shook up. How can our players' safety be put at risk at our place of work?"