La Celeste overcame the European champions at the Fisht Olympic Stadium on Saturday night to set up a World Cup quarter-final against France in a week's time.
Uruguay face being without one of their key players for that match in Nizhny Novgorod, though, as Cavani - who netted both of his side's goals against Portugal - was replaced 16 minutes from time after pulling up.
Asked for an update on the Paris Saint-Germain star's injury, Oscar told reporters at his post-match presser: "He was injured and he felt pain. I haven't spoken to the medical team because the match has only just finished.
"We don't have a lot of time to recover. Right now, we are only worried but we don't know how serious the injury really is."
Of the 45 international goals scored by Cavani, strike partner Luis Suarez has now assisted 12 of them.