The Argentina striker is said to have torn a muscle during a victory over Nigeria, a match in which Aguero was substituted after 38 minutes.
The injury, which could not be immediately confirmed by a team spokesperson, would be a significant blow to Argentina's ambitions at these finals as they attempt to win at the home of great rivals Brazil.
The Manchester City forward - who is part of Argentina's so-called "Fab Four" of strikers - had played in each of his country's matches as they progressed to the last 16 as leaders of Group F.
Alejandro Sabella, the Argentina head coach, would only confirm that his striker has suffered a muscle problem. Should Aguero be unable to play again in Brazil then it is expected that Ezequiel Lavezzi, the Paris Saint-Germain forward, will be afforded a place in the starting XI as his replacement.
Argentina next play in Sao Paulo on Tuesday, a last-16 meeting with Switzerland. "We have forwards of the same style as Aguero and others, with a different style, like Lavezzi, who came in and handled himself well on the wings and helped us cover spaces," said Sabella following that victory over Nigeria, in which Lionel Messi scored twice.