Vice-captain Upul Tharanga is the likeliest candidate to lead the team in Mathews' stead.
Mathews has not played internationals since January because of a hamstring complaint, and had also missed a tri-series in Zimbabwe late last year because of "multiple injuries" in his legs.
"Mathews had complained of stiffness and pain, prompting the team management to conduct radiographic investigations, which revealed a strain on the muscle," an SLC release said. "He will engage in supervised recovery over the next few days but will most likely sit out the first group stage match."
Mathews' absence would be a substantial blow to Sri Lanka, who rely on him to bring balance to the XI - he often delivers 10 overs in ODIs in addition to batting at No. 5. Mathews had also appeared to be in good batting form, having struck 95 off 106 deliveries against Australia in Sri Lanka's first warm-up encounter. He didn't play the second practice match against New Zealand.