He suffered the injury during the hosts' opening win against Zimbabwe last week and was left out of the rain-curtailed group defeat against South Africa on Saturday.
"We took an MRI scan on his left side and it showed a slight tear," Sri Lanka manager Charith Senanayake said.
"Mendis bowled a few overs at the nets today, but we will monitor him carefully and take a call whether he is fit enough to play against New Zealand."
Mendis returned Twenty20 record figures of six wickets for eight runs against Zimbabwe before going off the field.
- Charith Senanayake