According to Brad Townsend of the Dallas Morning News, Carlisle added that he has been fully vaccinated since January and that there is a "chance and a hope" that the result will come back as a false-positive.
Carlisle said he is at the team hotel in New York, but potentially could still coach in Friday's game against the New York Knicks if his new test results are negative.
Carlisle led the Mavericks to a championship in 2011 and has taken them to the playoffs on eight occasions, including last season.
With Luka Doncic and Kristaps Porzingis leading the charge, the Mavs own a 25-21 record this season, which is good for seventh place in the Western Conference.
Dallas is just one game up on the eighth-place San Antonio Spurs and three games up on the 10th-place Golden State Warriors, though, meaning it is far from guaranteed a spot in the playoffs or even a place in the postseason play-in games.
The Mavericks have two big games ahead of them this weekend, as they will face the Knicks on Friday, followed by a clash with the Washington Wizards on Saturday.
If Carlisle is unable to coach the next game or two, assistant Jamahl Mosley is in line to serve as the interim head coach, per Townsend.
Mosley would be backed up by fellow assistant coaches Darrell Armstrong, Mike Weinar and Jenny Boucek.