The Grizzlies issued a statement saying that Morant "will be away from the team for at least the next two games".
That will mean Morant will not play on Sunday against the LA Clippers or Tuesday against the Los Angeles Lakers.
A two-time NBA All Star and NBA Rookie of the Year in 2020, the 23-year-old Morant is seen as one of the brightest young talents in the league but has been involved in a series of off-court incidents.
"I take full responsibility for my actions last night," Morant said in a statement.
"I'm sorry to my family, teammates, coaches, fans, partners, the city of Memphis and the entire Grizzlies organization for letting you down.
"I'm going to take some time away to get help and work on learning better methods of dealing with stress and my overall well-being," he added.
In the Instagram Live broadcast in the early hours of Saturday morning, Morant was seen holding up a handgun.
Morant later deleted both his Instagram and Twitter accounts on Saturday.
The NBA said they were investigating the case while Morant's sponsors Nike issued a supportive statement.
"We appreciate Ja’s accountability and that he is taking the time to get the help he needs. We support his prioritization of his well-being," the company said.
But pundits were less forgiving.
"Ja Morant’s fault is his own, and I’m proud of him for owning it. But he needs to get it together," said ESPN's Stephen A Smith.
"It doesn’t matter where Ja Morant is from or how he grew up, he’s making truly catastrophic decisions," tweeted journalist Jemele Hill.
The incident comes just days after U.S. media reported that Morant had been accused in police reports last year of punching a 17-year-old.
No criminal charges were filed against Morant in the incident, which took place during a pickup basketball game at Morant's Tennessee house in July 2022. Morant's agent said he had been acting in self-defense.
In police records obtained by the Washington Post , the unnamed teenaged boy accused Morant of punching him "12-13 times" during a pickup basketball game at Morant's Tennessee house in July 2022.
In interviews with police the teen said that after their altercation Morant went into his house and "re-emerged with a gun visible in the waistband of his pants."
Morant told police he "swung first" but felt he was acting in self-defense after the teenager threw a basketball that hit him in the head, later making a comment that Morant found threatening.
"Any of the dozens of witnesses will confirm Ja acted in self-defense and that he did not have a firearm," said Morant's agent Jim Tanner.
Days before that incident, the head of security at a Memphis mall told police he felt "threatened" by Morant and a group of his associates after an incident in the shopping center's parking lot.
Morant was in the headlines again in early February, when the NBA investigated allegations by the Indiana Pacers that the player's entourage "aggressively confronted" members of their traveling party, possibly pointing a red laser at them.