Thousands of athletes and media personnel are arriving in the Japanese capital ahead of the global competition beginning on July 23.
There has already been a total of 44 coronavirus cases linked to the Olympics, including one overseas visitor who is involved in organizing the Games.
The person in question, whose nationality has not been disclosed for privacy reasons, is now quarantining for 14 days in a hotel room.
Tokyo 2020 CEO Toshiro Muto confirmed the news at a news conference on Saturday and added: "That positive cases arise is something we must assume is possible."
Around 11,000 athletes from 205 national Olympic committees are expected to stay at the Olympic Village over the next three weeks.
Speaking earlier this week, International Olympic Committee president Thomas Bach vowed Tokyo would host a "safe and secure" Olympics.
IOC official Joan Coates also insisted it was down to organizers to ensure the Olympic Village "is the safest place in Tokyo".
Following news of Friday's positive case in the camp, however, Games chief Seiko Hashimoto says it is understandable that some athletes may be concerned.
"Athletes who are coming to Japan are probably very worried. I understand that," Hashimoto said.
"That is the reason why we need to make full disclosure.
"We are doing everything to prevent any COVID-19 outbreaks. If we end up with an outbreak we will make sure we have a plan in place to respond."
The 2020 Games, delayed by a year, will be held mostly without spectators after a state of emergency was called in Tokyo amid rising coronavirus cases.
Another 1,271 new COVID-19 cases were reported on Friday, compared to 822 on the same day last week.