Competing for the Russian Olympic Committee (ROC) team, world No. 2 Medvedev appeared to be struggling during his third round men's singles match against Fabio Fognini of Italy.
Chair umpire Carlos Ramos asked Medvedev if he could continue playing, and the player responded: "I'm a fighter, I will finish the match, but I can die," he said. "If I die, is the ITF (International Tennis Federation) going to take (sic) responsible?"
CNN has contacted the ITF for comment.
Later Wednesday, Spain's Paula Badosa left the court in a wheelchair after being forced to retire from her women's singles quarter-final match against the Czech Marketa Vondrousova due to heatstroke.
Badosa lost the first set 6-3 before requiring a medical timeout ahead of the start of the second set.
After lengthy treatment, Badosa was unable to continue and retired from the match.
"I have suffered a heat stroke as you all have seen, and I did not feel fit to continue competing in the match," Badosa said in comments posted by Tokyo 2020.
"It was a shame to end my participation this way. The conditions have been demanding from day one, we tried to adapt as best as possible, but today the body has not resisted as needed."
After the match, Vondrousova revealed she is taking special measures to deal with the conditions.
"In the match, I use the ice towels and also use the air tube... it's very nice," she said. "I also have some gels."
Tokyo temperatures reached the upper 80s Fahrenheit on Wednesday.
"The risk for heat exhaustion and heat stroke remains," according to CNN's weather team, which added that the high humidity "makes it very difficult for the body to cool itself naturally."
25-year-old Medvedev also addressed the conditions after the match, which he won 1-6 6-1 6-3.
"Even from the first set, I didn't feel good enough with my breathing. That's why I called the physio. I felt like my diaphragm had blocked. I couldn't breathe properly. I think it was the most humid day we have had so far," he said in comments posted by Tokyo 2020.