The Manchester United winger was leading a first-half counterattack with a pacy, direct run from deep in his own area but pulled up after being crowded out of possession by three retreating Chile defenders.
After spending a minute or two on the ground he returned to the field of play but was quickly replaced by Paris Saint-Germain's Ezequiel Lavezzi.
The Argentine had been enjoying a fine patch of form in the latter stages of the Copa America, scoring two and setting up another in the 6-1 semi-final thumping of Paraguay.
But he lasted just 29 minutes of the final against hosts Chile on Saturday, which is a blow for his country as well as his club.
Manchester United resume pre-season training on Monday, and while Di Maria would have been afforded a break after representing his country at the Copa his preparations for the 2015-16 campaign may have been dealt a further blow thanks to this latest injury set-back.
The 27-year-old's first season in English football was blighted by injury. Having started well with his new club his form quickly tailed off, and he struggled to get back into the team after picking up a hip problem against Hull City at the end of November.
Already suffering a poor run of performances into the new year, he was shown a red card in an FA Cup clash against Arsenal in March and had to make do with substitute appearances for the remainder the season.
He had largely impressed for Argentina in Chile in recent weeks but now looks set for another set-back in what has been a frustrating 12-month period for the former Real Madrid man, who also missed the 2014 World Cup final through injury.