Shams Charania of The Athletic and Stadium reported the news.
Beasley, 30, was released by the Los Angeles Clippers after being traded by the Lakers at the deadline. He has gone unsigned since. His suspension would start once he is signed by an NBA team.
Typically, five-game suspensions are given to players who repeatedly violate the NBA's policy on marijuana.
Beasley was previously arrested in 2013 for marijuana possession while he was a member of the Phoenix Suns. He was also fined for possession of marijuana in 2011 while with the Minnesota Timberwolves but said it belonged to a friend. In 2009, Beasley went into a rehabilitation facility for stress-related issues.
"People meet me. First thing they say: 'You’re totally different than I thought you are," Beasley told reporters in 2017. "A large part of my career is due to perception, what people think what I am or should be. My past is my past. They keep harping on it. Everyone wants me to grow up and learn from my past, learn from my mistakes. But you guys should do the same thing. I’m years removed from any marijuana incident or incident period. But it’s all anybody speaks about. I’ve grown up. Now it’s time for you to grow up."
This is Beasley's first drug-related incident since that 2013 arrest in Arizona.
Beasley averaged 7.0 points and 2.3 rebounds per game last season with the Lakers. His 10.7 minutes per game were the fewest of his career.