The All Whites vice-captain will return to New Zealand on Tuesday after picking up the injury, which may require an operation, in Monday's 2-1 defeat in Melbourne.
The rest of Ricki Herbert's squad are leaving for a training camp in Austria and the New Zealand coach said he hoped Brown would still be able to join them in South Africa at the June 11-July 11 finals.
"We're hoping he won't be ruled out. We would fly him to South Africa, that's what I want," Herbert said.
"I'll give him as long as he needs but the problem is if he has surgery it's only three weeks to the opening game."
Brown's fellow midfielder Leo Bertos has been cleared to travel despite being the victim of two brutal fouls from Socceroos Vince Grella and Tim Cahill that sent him limping from the pitch at the Melbourne Cricket Ground.
New Zealand open their World Cup campaign against Slovakia in Rustenburg on June 15 before facing champions Italy and Paraguay in their other Group F matches.
