The test result was reported shortly before Utah's game against the Thunder in Oklahoma City was to begin, and that game was abruptly postponed.
The league said the affected player was not at the arena and was being treated by health officials.
"The NBA is suspending game play following the conclusion of tonight's schedule of games until further notice," the league said. "The NBA will use this hiatus to determine next steps for moving forward in regard to the coronavirus pandemic."
The Jazz issued a statement saying that the affected player had flu-like symptoms but initially tested negative for influenza and a respiratory infection.
The decision was made to test again for COVID-19. The player tested positive and is being treated by health officials in Oklahoma City.
"A preliminary positive result came back right before tip-off of the Utah Jazz-Oklahoma City game," the Jazz statement said. "The decision was correctly made by the NBA to postpone the game."
They declined to name the player in the statement, but Denver Nuggets coach Mike Malone told reporters he believed it was French defensive standout Rudy Gobert. Gobert was listed first as questionable for the game and then as out with illness.
"Rudy Gobert. You think it is not going to affect us, we are NBA," said Malone. "One of our players has the coronavirus. Who knows what that means for their team and the other teams that have been with them."
Team owners had been discussing Wednesday how the league should respond to the coronavirus outbreak.
Dallas owner Mark Cuban was sitting courtside at the Mavericks' game against the visiting Nuggets when he got the news on his phone.
"I thought this is crazy. It can't be true," Cuban said. "It is like out of a movie. Unreal."
Upon learning the season was being suspended, Cuban immediately walked over to the bench to let the team officials know.
"It is not about basketball and money. This is exploding to the point where I think about the families. We are making sure we are doing this the right way," he said.
"The idea that a couple of players have it .... it is stunning, isn't the right word."
Earlier NBA team owners and league officials had been wrestling with how to manage in the face of the outbreak, considering not only postponing games, but also playing without fans in the arenas.
The Golden State Warriors had confirmed they would host the Brooklyn Nets on Thursday in San Francisco behind closed doors after San Francisco city officials announced a two-week ban on all gatherings of more than 1,000 people.
The league-wide decision was made after the confusing scenes in Oklahoma City, where Jazz and Thunder players took the court to warm up, but shortly before the scheduled tip-off were sent to their locker rooms and police began to clear the Chesapeake Energy Arena.
Fans were told only that the game was postponed due to "unforeseen circumstances" before they were herded out of the arena.
Gobert's teammate Emmanuel Mudiay was also listed as suffering from an undisclosed illness on the team's injury report.
Six NBA games were scheduled for Wednesday. Four were underway when the game in Oklahoma City was called off and a later game between the New Orleans Pelicans and Kings in Sacramento was cancelled. The decision was made because of one of the officials had worked a Utah game earlier in the week.
"It's unprecedented," Detroit coach Dwayne Casey -- whose Pistons fell to the 76ers in Philadelphia -- said of the decision to suspend the season. "I think it's the prudent thing to do."
Cuban said he is ready to do whatever the league asks of him.
"I am not an expert," he said. "The NBA has people who specialize in this. They are talking to the CDC. I don't want to fake it."
Miami Heat coach Erik Spoelstra said this is much bigger than basketball.
"Stunned," Spoelstra said after his team lost to the visiting Charlotte Hornets.
"It's a very serious time right now. I think the league moved appropriately," added Spoelstra, who concluded his post-game press conference by saying: "There's nothing to really talk about with the game, right?"
Cuban said he was thinking of the safety and health of his family members.
"This is global pandemic. Peoples' lives are at stake. I am more worried about my kids and my 82 year old mother than when we play our next game."
Mavericks guard JJ Barea said he tried to block it out of his mind while the game against the Nuggets was on.
"It is like bad movie," Barea said. "We've got to be safe and learn from it.
"I've got little bit of fear. But you can only control what you can control. Tonight my job was to play basketball."
Nuggets player Paul Millsap said he was stunned by the news of the developments.
"It is a scary situation. Everyone is in shock," said Millsap.