The tourists have already replaced injured paceman Dhammika Prasad with Kusal Perera, while Shaminda Eranga's bowling action is being investigated.
England have already clinched a series victory over Sri Lanka by winning the first two of the three-Test series.
The third and final match starts at Lord's on Thursday 9 June.
Chameera has a stress fracture of the back, while Prasad has been ruled out with a shoulder problem.
Sri Lanka have called up uncapped left-arm seamer Chaminda Bandara, 29, for the third Test with England, to replace the injured Dushmantha Chameera.