Di Maria was substituted in the first half of Argentina's 5-0 demolition of 10-man Panama in Group D, and the 14-time Copa champions confirmed the attacker sustained a right-leg injury in Chicago on Friday.
Argentina are now awaiting scans to determine the severity of the injury.
Di Maria played a leading role in the first half, delivering the free-kick for Nicolas Otamendi to open the scoring in the seventh minute at Soldier Field.
The 28-year-old Paris Saint-Germain star was then forced from the field two minutes before half-time, replaced by Erik Lamela.
Argentina captain Lionel Messi came off the bench in the second half and scored a hat-trick, while Sergio Aguero completed the rout in the 90th minute as last year's runners-up won through to the knockout round of the centenary tournament.