Odom, the Clipper's leading scorer last season, was to serve the second game of a five-game suspension Wednesday night when the Clippers faced the Memphis Grizzlies.
He is eligible to return Nov. 16 against the Toronto Raptors.
The NBA does not disclose information about the testing or treatment of any player in the program, but Odom volunteered the information following the Clippers' shootaround with his coaches and teammates present.
"I chose to experiment with marijuana, that's why I'm here right now," he said after stating he doesn't have a drug problem.
"I'll be receiving counselling. That's not rehab."
Odom, who turned 22 Tuesday, choked up within seconds of addressing reporters and was quickly comforted by teammates.
"I'm here today because I failed," Odom said. "I'm disappointed in myself.
"I don't want to put anybody in this position again. I'm sorry, but I don't want everybody to feel sorry for me."
After his first five-game suspension was announced March 7, Odom vowed he would never again miss a game in such a manner.
"I made the mistake once, now it's twice," he said. "I feel like I can get through it, I know I can get through it, I'm strong enough.
"Nothing I can say is going to make people believe me, I've just got to do it."
Tearful throughout the 13-minute news conference, Odom said he didn't expect the kind of support he received "because I've been through this before."
"This is genuine support," Clippers forward Elton Brand said. "We came here collectively as a group because we want to support him, he needs us right now.
"We're going to continue when he comes back to support him also."
Clippers coach Alvin Gentry also said the support for Odom would not waver.
"He's a good person, and everybody here believes that," Gentry said. "We love him because of who he is and that's the way it's going to be.
"We believe in him, we believe in him until the day we die.
"All we can do is help any way we can. We've got to make sure he's better as a person, the basketball part is irrelevant right now.
"When Lamar comes back, he's going to be a good player."