The 23-year-old, who was forced to sit out of yesterday's World Cup final defeat to India, has been ruled out of the lucrative Twenty20 tournament with a side strain.
Matthews was due to play for IPL team Pune Warriors after securing a USD 9,50,000 contract.
He picked up the right-side strain during the World Cup semi-final win over New Zealand in Colombo.
"I have pulled a muscle. I am finding it difficult to walk, it will take about eight weeks to heal," Matthews told reporters in Colombo after the team arrived from Mumbai.
Sri Lanka lost the final last night at Mumbai's Wankhede Stadium after India reached 277 for four in 48.2 overs, surpassing Sri Lanka's 275 runs with 10 balls left.
The all-rounder had previously played for the Kolkata Knight Riders.