All-Star guard Morant, 23, appeared to hold up a handgun in a live broadcast on his Instagram page on Saturday.
It occurred hours after the Grizzlies lost 113-97 to the Denver Nuggets.
Morant, who has been suspended for “at least two games”, apologized and said he would “get help”.
“I take full responsibility for my actions last night,” he said in a statement.
“I’m sorry to my family, team-mates, 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.”
NBA spokesman Mike Bass said, “We are aware of a social media post involving Ja Morant and are investigating.”
In a statement, the Memphis Grizzlies said that “Ja Morant will be away from the team for at least the next two games”.
The Grizzlies, who are second in the Western Conference, face the Los Angeles Clippers on Sunday and the Los Angeles Lakers on Tuesday in their next two fixtures.
Morant is averaging 27.1 points and 8.2 assists per game this season and made his second consecutive All-Star Game appearance last month.