Swiss striker Frei suffers broken arm
"It must be calculated that Frei will not be able to play football for between eight and 10 weeks," said the club on their website.
The 30-year-old was operated on Saturday night after suffering the injury early during the day's 2-1 win over Aarau in the Swiss Super League.
Frei, who joined Basel from Borussia Dortmund this season to be certain of regular first-team football, has scored 40 goals in 73 appearances for his country.
Switzerland, who reached the second round in 2006, face Spain, Chile and Honduras in their World Cup group in South Africa in June.
"It's something we have to live with," said Switzerland coach Ottmar Hitzfeld on the Swiss federation's website.
"We still have some alternatives up our sleeve. But I hope for the player, the club and the national team that his recovery goes well."
Frei 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.