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Lakers spokesman John Black said Thursday that Dr. Neal Elattrache, a shoulder specialist, examined Brown a day earlier and made the diagnosis.
Brown, 24, hasn't played since colliding with Andrew Bynum during practice Saturday. His shoulder bothered him last season as well.
Brown, the No. 1 pick in the 2001 NBA draft by the Washington Wizards, averaged 7.4 points and 6.6 rebounds in 72 games for the Lakers last season -- his first with the team. He became the team's starting center after Chris Mihm injured his right ankle March 12.
Mihm played only one game after that and is still recovering from offseason ankle surgery.
"Chris won't be ready by opening night," Black said. "We really don't want to put a timetable on it other than to say it's going to be more than two weeks."
The Lakers open the season Oct. 31 against the Phoenix Suns.
With Brown and Mihm sidelined, possible options at center to start the season are the 18-year-old Bynum, Ronny Turiaf and Brian Cook. Bynum was the team's first-round draft pick last year and Turiaf was the second-round selection. Neither played much as rookies, and Cook is a natural forward.
"It's a coaching decision," Black said.
Defending NBA scoring champion Kobe Bryant, recovering from offseason knee surgery, hopes to be ready for the season opener, but he hasn't played in the preseason.
"Our hope is he'll get to play in at least one preseason game," Black said, adding that Bryant was "probably doubtful" for Sunday night's game against the Suns in San Diego. The Lakers have one preseason game after that -- against Denver next Thursday night in Anaheim.
The Lakers have several other injured players, including Vladimir Radmanovic (sprained ligament in his right hand); Shammond Williams (abdominal strain); Aaron McKie (disc irritation and inflammation), and Von Wafer (bruised left heel).
Lakers coach Phil Jackson, who had hip replacement surgery Oct. 3, has been working part time and is expected to be on the bench for the season opener.