The Paris Saint-Germain striker, however, then limped out of the action - with Ronaldo helping him off the pitch - and was replaced after 74 minutes.
The player told reporters after the final whistle he hurt his calf and Tabarez conceded he is unsure whether Cavani will be fit to face France in Friday's quarter-final.
"He was injured. He felt pain," Tabarez said at a news conference.
"I don't know exactly. I haven't spoken to the medical team. We won't have a lot of time for recovery.
"After resting, we will see what we have to do. Right now, we're only worried but we don’t know for sure how grave the injury is."
Uruguay and France don't play until Friday, giving the 31-year-old nearly a week to get fit, though his country will be nervously waiting for the results of medical scans.