The 53-year-old announced the news on his official Twitter account, writing: "We've been on full quarantine, our entire house now, for well over two weeks.
"I encourage everyone to do the same. Let's get this thing. Let's nail this thing. I'm an example of someone who has been able to fight through it.
"I'm doing absolutely fine. Thoughts and prayers to people who are struggling with this."
McEnroe, the younger brother of seven-times grand slam champion John, won the Roland Garros doubles title in 1989, and also reached the semi-finals of the 1991 Australian Open in singles.