The midfielder was replaced by Enzo Perez after 30 minutes of his side's quarter-final win against Belgium on Saturday, with officials confirming that Di Maria was struggling with a thigh injury.
It had been hoped that he would improve in time to play some part of the semi-final against the Netherlands on Wednesday, though reports in his homeland and Spain - where he plays for club side Real Madrid - have since suggested that the 26-year-old will play no further part in the finals.
Di Maria was awaiting the results of a scan last night. "Tests will be made today to assess the extent of the injury," read a statement from the Argentina Football Federation.
The Argentine has proven himself to be his side's most creative player - when Lionel Messi is taken out of the equation, at least - with his pace and vision having been fashioned into weapons in Brazil. He also links up well with Messi and the other forwards and has an eye for goal, as he proved when he scored decisively in the 1-0 win over Switzerland in the last 16. "He's vital, almost irreplaceable," said Alejandro Sabella, the Argentina head coach, ahead of the tournament.
Should Di Maria be ruled out for the denouement, Sabella will have to identify a replacement capable of unlocking a resolute Dutch defence in Sao Paulo. The coach will also be hoping that forward Sergio Aguero, who has missed Argentina's last two matches through injury, is fit enough to play some part in the game.
Sabella can at least find some solace in the return to form of striker Gonzalo Higuain. The Napoli striker scored expertly against Belgium to 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 in the competition, having scored four times in South Africa. "I wasn't getting desperate about scoring because I knew I was going to get a goal sooner or later," said Higuain, who ended a six-match scoring drought in Brasilia.
"I'm very happy, especially with this being such a historically important win for Argentina. They have 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."
The striker had first to convince himself of his fitness, having picked up an ankle injury before leaving Italy to head for the finals. "I very nearly didn't make it to the World Cup at all, but fortunately everything has worked out and I've been able to get that goal," he added.
He may be required to get another against the Dutch on Wednesday, though he has an able supporting cast. Including Messi. "The important thing is that we have reached our first goal - to be among the final four," said the Barcelona forward.