The NBA announced the suspension Tuesday, two days after Bynum was ejected for the foul in the two-time defending champions' 36-point loss to the Mavericks in Game 4.
The NBA also fined Bynum $25,000 for "removing his jersey and the manner in which he left the court."
The infraction will cost him $702,272 overall, including the fine.
Bynum expressed remorse for his actions Tuesday, saying his actions were terrible and unacceptable.
"My actions ... don't represent me, my upbringing, this franchise or any of the Laker fans out there that want to watch us and want us to succeed," Bynum said. "Furthermore, and more importantly, I want to actually apologize to J.J. Barea for doing that. I'm just glad that he wasn't seriously injured in the event and all I can say is, I've looked at [the replay], it's terrible and it definitely won't be happening again."
With 8:21 left in Game 4 of the Western Conference semifinal series, and the Lakers down by 32 points, Barea beat Steve Blake off the dribble, drove the lane and soared to the basket for what looked like an uncontested layup. But the 7-foot, 280-pound Bynum closed in and threw a right elbow into the 6-foot Barea's ribs. Barea flew sideways to the court and remained there writhing in pain.
The sixth-year center's initial attempts to contact Barea and apologize personally have gone unfulfilled, but he plans on continuing to try to get in touch with him.
"I think he has bigger and better and more important things to do, so I don't know if I'll get a response back, but I will [try to reach him]," Bynum said.
Bynum was expecting a suspension from the league.
"I believe I will be suspended. I don't want to be suspended," Bynum said earlier Tuesday.
He was suspended for two games in March for committing a similar foul on Minnesota's Michael Beasley. The NBA weighs a player's discipline history when doling out a subsequent suspension.
Information from ESPNLosAngeles.com's Dave McMenamin and The Associated Press was used in this report.