"He needs rest for about four weeks and physiotherapy," manager Kushil Gunasekera told AFP.
The off-spinner will return to Colombo as scheduled on Sunday from his English county duties at Lancashire and be examined by Sri Lankan team physio Tommy Simsek.
"The next course of action will depend on his (Simsek's) advice," Gunasekera said, adding that Muralitharan had told him over the telephone that rest was all he needed to regain fitness.
"He is said to be having a torn tendon on his right bicep," Gunasekera said.
Muralitharan was on Wednesday ruled out of the ICC World Twenty20 championships in South Africa next month following muscle pain on his right shoulder. But he should be fit for the two Tests against Australia in November where he needs nine scalps to overtake the retired Shane Warne's world record tally of 708 wickets.