Bok blow for Toulon
The 35-year-old picked up the injury during last Saturday's 21-25 Top 14 loss to Brive and will undergo surgery on Tuesday.
Smith's injury is the latest blow for the 2016 finalists who have had a terrible start to their campaign being beaten twice in their first three matches.
His absence follows that of Australian wing Drew Mitchell and South African Bryan Habana away on international duty - with the injury list already including James O'Connor, Anthony Étrillard, Matt Giteau, Ayumu Goromaru, Duane Vermeulen and Jean-Charles Orioli.
Agence France-Presse