Rotterdam tournament director Richard Krajicek released the 21-year-old from his contract so he can take part in the basketball showpiece in New Orleans.
"Kyrgios prefers his passion beyond his profession," said Krajicek.
Kyrgios is suspended for eight weeks from the ATP Tour for not producing his "best effort" in Shanghai last week.
The world number 14, who had won the Japan Open the previous week, patted the ball over the net several times when serving in his 6-3 6-1 second-round defeat by Mischa Zverev in China.
He also began walking back to his chair before a Zverev serve had landed.
Kyrgios subsequently said he was "truly sorry" and would use this time during his suspension "to improve on and off the court".
The sanction, which included a fine of $25,000 (£20,560), will keep him off the tour until 15 January, although he could return by 7 November if he agrees to an ATP plan that he consults a sports psychologist.
Krajicek, the 1996 Wimbledon champion, has added US Open champion Stan Wawrinka to the Rotterdam field in place of Kyrgios.
"We wanted to hold [Kyrgios] to his contract," the Dutchman told the Nederlandse Omroep Stichting.
"You see what can happens when he is tired and [tennis] has little meaning, as in China. We do not want that. So we decided to terminate his contract. We want a top tennis player seen on the court. Kyrgios prefers his passion beyond his profession.
"If every week he is focused on tennis, he might be mentally burned out after six months. He needs an outlet."
Kyrgios represented his country at youth level as a basketball player, and said in an interview in June 2015 that he preferred the sport to tennis.
Asked then if he might have had a career in basketball, Kyrgios said: "I thought I was going to.
"I was trying to get there when I was 14 and every time when I'm playing now, I still think I can for some odd reason, even though I'm playing a completely different sport.
"That's just the way it is and unfortunately I think my basketball career has come to an end."
The NBA celebrity match is part of the organisation's All-Star weekend. It features three matches, culminating in the prestigious All-Star Game on 19 February, involving the NBA's top players.
This year's weekend was originally to have been held in Charlotte, North Carolina, but was moved after state legislators introduced laws that limited anti-discrimination protections for lesbian, gay, bisexual and transgender people.
Australian Nick Kyrgios has pulled out of the Rotterdam Open to play in basketball's NBA All-Star Celebrity Game next February.