Mathews is not a part of the Sri Lankan T20 side that will host Bangladesh in a two-match T20 series starting April 4 in Colombo.
Apart from hamstrong injury, Mathews' return will be delayed by calf strain.
"At this stage I think I can say Angelo will not play the T20s," SLC cricket manager Asanka Gurusinha told ESPN Cricinfo.
"The IPL will be affected because he has to wait for the physio and the trainer to give him the green light. He has to be 100 percent fit. Angelo has to make that call with the physio, because if he's not 100 percent fit, we will not let him go."