The eight-time Ballon d'Or winner hurt his ankle in the 36th minute of the final against Colombia but soldiered on until the 66th minute when he limped off the field in tears, before strapping an ice pack to his swollen ankle on the bench.
With the game finely poised at 0-0 when he departed, Argentina raised their game and Lautaro Martinez struck in extra time to secure a 1-0 victory and a record 16th Copa title.
Skipper Messi went on to lift the trophy alongside longtime teammates Angel di Maria and Nicholas Otamendi, both 36.
"Leo is the greatest player in history. He never wants to leave the pitch. He has a swollen ankle and he wants to keep on playing," Argentina coach Lionel Scaloni told reporters.
"I prefer those players and his teammates see that, that he is 30-something-years-old and he's there and he wants to contribute. He wants to play not because he is egotistical or selfish.
"He wants to continue playing because he doesn't want to leave his teammates. He doesn't want to leave them on the pitch even when he's in that condition... He doesn't feel well when he has to leave and he was born to be on the pitch."
Messi has hinted at retirement on several occasions in recent months, saying this week that he and his fellow Argentine veterans were fighting their "last battles" at the Copa América.
"I know Leo (Messi), I know how he thinks. He always wants to be there, but the fact that he's part of this team is the best thing for us," midfielder Rodrigo De Paul told TyC Sports.
"With Fideo (Di Maria), I'm sad to see him go, but I'm also happy because he's one of the few that can say goodbye in this way as a World Cup and Copa champion."
