The league also fined the Timberwolves organization $50,000 Friday for what it called inappropriate comments.
In an interview with 1500 ESPN Twin Cities, Kahn said the recently acquired Beasley used "too much marijuana" in the past but Minnesota's new power forward is maturing and was worth acquiring from Miami despite his off-court issues.
"He's a very young and immature kid who smoked too much marijuana and has told me that he's not smoking anymore," Kahn said in the interview, "and I told him that I would trust him as long as that was the case."
After one year at Kansas State, Beasley was the No. 2 overall draft choice of the Heat in 2008. Just 21 years old, he was traded two weeks ago to the Wolves, who hope a change of scenery and a move to a young team will bring out his considerable talents.
At his introductory news conference July 15 in Minnesota, Beasley said because of his spotty past -- he got kicked out of the NBA rookie symposium, was fined for breaking Heat rules and last summer entered substance-abuse treatment in Houston -- he might be a bit misunderstood.
"I feel like I did good my last two years in the NBA playing for Miami," said Beasley, who averaged 14.3 points per game and 5.9 rebounds in two seasons with the Heat. "But I feel like there's a lot that the world don't know about me. A lot of my game hasn't been shown. A lot of my personality hasn't been shown. I feel like it's a new beginning and a fresh start and I'm ready to start my life."
Kahn said he believes Beasley has made strides working to eliminate some of his past problems. Were Beasley in his late 20s, the Timberwolves' president said he might not have considered trading for him. It cost the Wolves only two second-round draft picks and cash considerations to acquire Beasley.
"He has developed a really good support system around him this past season in Miami," Kahn told 1500 ESPN Twin Cities. "He has hired people to help him grow up. He is growing up -- he's not grown-up. He's 21 ... and if you think back, as I do all the time, to when I was 21, and if you had given me this kind of money and put me in this kind of world with these kinds of pressures attached to it and some of the demands, I don't know how well I would have handled it, any easier than, say, he has.
"I think that if Michael was 25 or 26, maybe I would have felt differently," Kahn said. "Some of these kids simply deserve the opportunity to make mistakes and grow up."
Both the Timberwolves and Kahn declined to comment on the fines through a team spokesman.
Information from The Associated Press was used in this report.