As Medel shielded the ball out of play for a goal kick, Messi gave the defensive midfielder a small shove.
Medel, renowned for his short fuse, reacted furiously and confronted Messi, bumping his shoulder into the Argentine while leaning his head forward.
Messi held his hands up to proclaim his innocence as the shorter Medel proceeded to barge into Messi’s chest four times.
The five-time Ballon d’Or winner did not respond to any of the provocation, leaving his arms raised until other players came to intervene.
However, referee Mario Diaz de Vivar rushed over to the incident and hastily brandishes red cards to both Messi and Medel.
Both players seemed shocked at the decision and while Messi held out his arms in bemusement, Medel sought out the official but was restrained by team-mates.
Seven Argentina players surrounded Diaz de Vivar as his assistant joined his side, trying to calm the situation.
Several little disagreements played out between both teams as management eventually flooded onto the field to try to resolve the vitriol.
After much dispute, Messi and Medel eventually left the field in what was already an action-packed match-up.
Manchester United forward Alexis Sanchez was taken off in the 17th minute after going down and holding his hamstring grimacingly.
That contributed to Chile’s woes as Sergio Aguero and Paulo Dybala had given Argentina a 2-0 lead before Messi’s sending off.
The red card capped a disappointing tournament for Messi, who was unable to inspire his compatriots to his first international trophy.
Messi originally retired from international football in 2016 but reversed his decision following widespread pleas from his homeland.
Brazil legend and World Cup winner Rivaldo feels sympathy for the Argentine, telling Betfair before the third-place tie: “Right now, Lionel Messi should feel sad after fighting so much for his national team and losing yet again.
“Argentina hasn’t won the Copa America since 1993 and Messi wanted this title very much.
“I’m sorry for him as he represents so much for football and it’s disappointing to see him not achieving one of the remaining goals in his career.”