Brown suffered the injury in practice Friday prior to a 97-91 loss to the crosstown rival Clippers. He played 25 minutes but managed just two points and eight rebounds.
"I tried to make a quick push and it gave a pop on me," Brown said. "They say two weeks, but two weeks is a long time. It's going to be boring as [anything] sitting at home."
The top overall pick in the 2001 draft by the Washington Wizards, Brown was hoping to start his career anew after being traded to the Lakers in the offseason. But the 23-year has struggled, averaging just 5.9 points and 6.2 rebounds in 28 minutes.
The 6-11 Brown's best season was 2003-04, when he averaged 10.9 points and 5.0 rebounds for Washington. He was sidelined early last season with a broken bone in his right foot and a strained right ankle tendon.