Mathews sustained the injury in a Twenty20 international at the Wanderers on January 22, when he completed a half century, despite limited mobility, to lead Sri Lanka to victory by three wickets.
The selection committee will meet on Tuesday to decide on the composition of the squad and who should replace him as skipper, Sri Lanka Cricket (www.srilankacricket.lk) said on its website.
The Sri Lankans will start the tour against a Prime Minister's XI in Canberra on February 15 before Twenty20s against a weakened Australia team in Melbourne, Geelong and Adelaide.
The series has been somewhat devalued by the fact that Australia's top players will be in India preparing for a test series rather than playing against the Sri Lankans.
