Both the Titans and Minnesota Vikings, who played host this past Sunday in Minneapolis, "will suspend in-person club activities starting today," according to the joint statement.
The Titans are next scheduled to host the Pittsburgh Steelers and the Vikings are supposed to take on the Houston Texans. Both games are set for 1 p.m. ET on Sunday.
The statement did not mention if those upcoming contests will be played.
"All decisions will be made with health and safety as our primary consideration," according to the union and league. "We will continue to share updates as more information becomes available."
The NFL has completed three weeks of games, which have been played largely inside empty stadiums.
The league's COVID-19 protocols do not spell out exactly how many players would need to test positive for a game to be postponed.
"There is no algorithm for postponing a game," NFL spokesman Brian McCarthy said in a statement to NBC News. "We will monitor and evaluate the situation on a day-by-day basis."
If the Titans-Steelers game has to be postponed, the NFL would have a viable option to reschedule. Tennessee is off on Sunday, Oct. 25, which is the same day as Steelers are set to play the Baltimore Ravens.
Both the Steelers and Ravens have bye weeks on the following Nov. 1, so the NFL could move this Sunday's Titans-Steelers game to Oct. 25 and push Pittsburgh-Baltimore to the following weekend.
This is a developing story, please refresh here for updates.
This article was originally published on NBCNews.com.