The 29-year-old who missed a penalty shootout made the decision after La Albiceleste lost their fourth major final in nine years.
“It’s not meant for me. For me the national team is over. I’ve done all I can, it hurts not to be a champion,” the Barcelona star said after defeat by Chile.
Despite winning over 12 major titles with Barcelona, Messi’s only major international honour is the 2008 Olympic gold.
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Argentina lost to Germany in the 2014 World Cup final in Brazil before two Copa America final defeats by Chile on penalties. Messi was also part of the Argentine side that lost to Brazil in the 2007 Copa America final.
“It’s been four finals, I tried. It was the thing I wanted the most, but I couldn’t get it, so I think it’s over,” he added.
“I think this is best for everyone. First of all for me, and then for everyone. I think there’s a lot of people who want this, who obviously are not satisfied, as we are not satisfied reaching a final and not winning it.
“It’s very hard, but the decision is taken. Now I will not try more and there will be no going back.”
Messi netted five times in the tournament to become Argentina’s record goalscorer with 55 goals.
After Sunday’s match finished 0-0 in 120 minutes, Chile won 4-2 on penalties.