It is expected that James will miss several games, sources told ESPN's Adrian Wojnarowski.
"Obviously, it's a huge loss," Lakers coach Frank Vogel said in his pregame remarks Tuesday. "It's disappointing. We just want the best for him right now. That's where our thoughts are. And we have a next man up mindset."
Talen Horton-Tucker started in James' place and scored two points in 16 minutes.
Vogel said the team found out James was entering the health and safety protocols on Tuesday morning and arranged for transportation for James to return to L.A. from Sacramento.
"Hopefully, this is something that's short term," Vogel said. "We'll see."
Vogel declined to answer a reporter's question about what symptoms James is experiencing, but Anthony Davis was more forthcoming in his postgame remarks.
"He said he's good," Davis said after leading L.A. with 25 points in James' absence. "I think he's asymptomatic, which is a good sign, but we want to make sure that he gets back. Health is most important. This is bigger than basketball. He has a family. We want to make sure that he's good no matter what."
Russell Westbrook, who had 23 points and six assists in the win, said he planned to call James after the game.
"I know he wants to play, he wants to compete," Westbrook said. "Just check his mental and making sure that he's in a good space because it could be difficult, you know what I mean? Especially coming in and out of the lineup."
James already has missed 12 of the Lakers' 23 games because of injuries and a suspension. L.A. is 7-4 with James this season and 5-7 without him.
"We know he wants to be in there every night," Vogel said. "More than anybody in the league, probably."
If a player has a confirmed positive test for COVID-19, the NBA mandates a minimum of 10 days of isolation away from his team without any physical activity. After that period, a player must undergo a cardiac screening and reconditioning in order to be cleared to return to the court. A player who tests positive also could clear protocol by returning two negative polymerase chain reaction (PCR) tests within a 24-hour period.
James revealed on Lakers media day in late September that he had received the COVID-19 vaccine.
"I know that I was very skeptical about it all," he said. "But after doing my research and things of that nature, I felt like it was best suited, not only for me but for my family and my friends. And that's why I decided to do it."
Vogel said he, Lakers vice president of basketball operations and general manager Rob Pelinka and team doctors met with Lakers players to emphasize the NBA's recommendation to receive booster shots to combat COVID-19.
"We met early in the season or right around the day or two of that recommendation," Vogel said. "Just to encourage and recommend the booster shot and the values that come with it."
James is averaging 25.8 points, 6.8 assists and 5.2 rebounds this season, his 19th in the NBA.
"It's an 82-game season," Vogel said. "You're going to have to deal with guys going in and out of the lineup. We've been without him some already this season. I feel like we're further along with our cohesiveness now than we were the first time he went out with his ab strain. And we got to come in and compete and get a W tonight."
L.A. trailed the Kings by as many as 13 in the second quarter before Vogel lit into his team at halftime, challenging the Lakers to play with better effort. They responded by outscoring Sacramento 67-33 after the break.
"We can't catch a break," Davis said. "But we still got to find ways to win. We can't let that affect us. Obviously he's a huge part of our team, but we've played a huge amount of games without him, so we kind of know how that is already. But we gotta continue to play like we did on the defensive end until he's able to come back."