The 61-year-old Carlisle, who was fully vaccinated in January, called the positive test result "unexpected."
"There's a chance and a hope that it will be a false positive," Carlisle told reporters before Friday's game. "This seems like possibly a mistake, but for these reasons I'm entering the [NBA health and safety] protocol."
During the virtual news conference, Carlisle said he is experiencing no symptoms.
"I feel great," he said. "I worked out earlier this morning. But this is just one of those situations where we've all got to be light on our feet."
Mavericks assistant Jamahl Mosley replaced Carlisle as head coach against the Knicks.
Dallas has a 25-21 record this season and sits at seventh in the Western Conference standings. The Mavs held a 49-46 lead over the Knicks at halftime Friday night.