Another paceman, Shaminda Eranga, was recently suspended for an illegal action.
The 29-year-old Pradeep, who has played 21 tests, was the lone frontline paceman at Pallekele, which the hosts won by 106 runs to take a 1-0 lead against the world's top-ranked side in the longest format.
The victory was a welcome one for Sri Lanka, who lost their two previous test series in New Zealand and England.
The right-arm bowler, who took two wickets in the first innings of the series opener, suffered the injury during training on Monday.
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"He has a slight hamstring strain on his right leg. His fitness will be assessed tomorrow (Wednesday) morning," Sri Lanka team manager Charith Senanayake told Reuters.
"He could be doubtful but we haven't taken a decision yet."
Sri Lanka fielded three frontline spinners at Pallekele and were always likely to load their attack with slow bowlers for the second test.
(Reporting by Sudipto Ganguly in Mumbai; Editing by John O'Brien)
