Di Maria had to be replaced by Enzo Perez after half an hour of Saturday's 1-0 quarter-final victory over Belgium, which set up a last-four clash against the Netherlands, when he damaged a muscle in his right thigh shooting on goal.
Media in his native country and in Spain, where he plays for Real Madrid, reported the 26-year-old would play no further part in the finals in Brazil, although there was no immediate confirmation from the Argentine football federation (AFE).
"Tests will be made today to assess the extent of the injury," the AFE said on their website on Sunday.
Nicknamed "Fideo" (Noodle) due to his slight frame, Di Maria is Argentina's most creative player after captain Lionel Messi.
His electric pace can carry him past and away from opponents, he links up well with Messi and the other forwards and he has an eye for goal as he proved when he netted the winner in the 1-0 win over Switzerland in the last 16.
"He's vital, almost irreplaceable," coach Alejandro Sabella said before the World Cup.
Should he be ruled out, Sabella will have to rely on Di Maria's replacement in the starting lineup to help unlock a well-drilled Dutch defence in Sao Paulo on Wednesday.
He will also be hoping forward Sergio Aguero, who has missed Argentina's last two matches through injury, is fit enough to make an appearance.
One obvious bright spot for Sabella is the return to goal-scoring form of striker Gonzalo Higuain, whose superb strike against Belgium put Argentina through to the semi-finals for the first time since 1990.
It was Higuain's first goal in five appearances at this World Cup and his fifth overall at football's global showpiece after he netted four in South Africa four years ago.
"I wasn't getting desperate about scoring because I knew I was going to get a goal sooner or later," Higuain, who ended a six-match scoring drought in Brasilia, told reporters.
"Obviously I'm very happy, especially with this being such a historically important win for Argentina," he added.
"They've been asking me since day one when the goal was going to come and I've always given them the same answer: I’m working on it."
(Editing by Ed Osmond)
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