The sanction comes after Morant met with NBA Commissioner Adam Silver in New York to discuss his conduct. The two-time All-Star previously said he planned to take some "time away" and apologised for the incident.
"Ja's conduct was irresponsible, reckless and potentially very dangerous," Silver said in a statement announcing the suspension.
"It also has serious consequences given his enormous following and influence, particularly among young fans who look up to him.
"He has expressed sincere contrition and remorse for his behavior. Ja has also made it clear to me that he has learned from this incident and that he understands his obligations and responsibility to the Memphis Grizzlies and the broader NBA community extend well beyond his play on the court."
A league investigation of the March 4 incident did not conclude that the gun belonged to Morant, was brought by him into the nightclub or was displayed by him beyond a brief period.
The investigation also did not find that Morant possessed the gun while traveling with the team or in any NBA facility. Colorado authorities did not find sufficient cause to charge Morant with a crime.
Morant is averaging 27.1 points, 8.2 assists and 6.0 rebounds in 53 games this season for the Grizzlies, who currently sit second in the Western Conference
