"I just felt something at one point and couldn't recover. I hope (to be fit), I'll do everything to make sure I can take to the field with my teammates," Cavani told journalists after the game.
"It hurts a little bit, but we will see how it looks tomorrow (Sunday)."
Uruguay are due to play France in the last eight on Friday in Nizhny Novgorod, and veteran coach Oscar Tabarez said he was "worried" for Cavani. He had to be helped off the pitch by Portugal skipper Cristiano Ronaldo and was replaced by Cristhian Stuani in the 74th minute of the game at the Fisht Stadium.
"Our next game is in five days which is not a lot of time, but after today we will rest. Obviously we are worried but we don't know exactly what the problem is," Tabarez said.
Cavani headed in a Luis Suarez cross to open the scoring in the seventh minute and then curled in a brilliant 62nd-minute winner after Pepe had equalised for Portugal.
"It was a mistake from us that cost us the equaliser but luckily we found some space and the team stayed strong mentally," said Tabarez.
"I am very pleased, we prepared for this, the injury was an inconvenience and we will see how it evolves."
Uruguay's formidable defence will now hope to stand up to the threat of the French attack, after Kylian Mbappe inspired them to a thrilling 4-3 win over Argentina earlier on Saturday.
"Now we have a very strong opponent in France. I can't give a very in-depth analysis because I was getting dressed while their game was on and in the last 15 minutes I was giving my team-talk.
"But I think France's strong point is their attack with (Antoine) Griezmann and Mbappe and their exceptional pace. If you give France space it becomes very difficult."
Tabarez added: "We didn't presuppose anything coming here. The players came to play seven matches. We will see if we can do it."