The striker was helped off the pitch at the end of the quarter-final first leg in Germany after collapsing with an injury to his right ankle.
Rooney will go for a scan later this week to discover the extent of the damage.
With the World Cup just over two months away, England head coach Fabio Capello would have been hoping his star player was not too badly hurt.
Capello expects to speak to Rooney tonight or tomorrow morning.
He told Sky News: "We have to wait for the scan, it's too early to tell at the moment.
"I need to speak to someone at Manchester United about it, but I'm never happy when an England player is injured because it's not the best thing for me."
Rooney left the stadium on crutches wearing a protective boot, but United boss Sir Alex Ferguson did not give much away when asked about the injury.
Speaking immediately after the match, Sir Alex said: "He's obviously hurt his ankle. It is too early to say. I don't think it's terribly serious, but we'll wait and see."
The injury to Rooney capped off an evening to forget for his side after Bayern Munich snatched a 2-1 win, thanks to a last-minute goal from Ivica Olic.
England have fitness doubts about a number of their squad ahead of South Africa, with midfielder David Beckham already ruled out and left back Ashley Cole yet to return from a broken ankle.
It will not be the first agonising wait England fans have had over Rooney's fitness, after he broke a bone in his foot just before the 2006 World Cup.
The 24-year-old eventually went to the tournament only to be sent off against Portugal as England went out on penalties.
Rooney has not had the best of luck in international competitions. Two years earlier he went off injured in the quarter-finals of Euro 2004.