Frei doubtful for Swiss opener
However, Frei was allowed to travel with the squad who are expected to arrive in Johannesburg on Thursday, Swiss media reported.
Switzerland coach Ottmar Hitzfeld said he hoped the injury was not ligament damage.
"I leave in the belief that he will take part in the World Cup. He perhaps will not be ready for the first match but I will be able to call upon him after that," he said.
Hitzfeld added that Frei suffered the injury trying to tackle team mate Steve Von Bergen. The striker remained on the ground for about five minutes before being taken to hospital.
Team doctor Cuno Wetzel said the Basel FC player has a bruised and sprained ankle.
The latest setback comes after a series of injuries that have plagued Switzerland's record scorer. In February, the 30-year-old had surgery after suffering a broken arm during a league game and was out for 10 weeks.
He also suffered a knee injury during Switzerland's opening game of the 2008 European championship, which the country co-hosted with Austria, and missed the rest of the tournament.
Switzerland, who must also play Chile and Honduras in Group H at the World Cup, start their campaign on June 16 against the European champions and tournament favourites Spain.