Pradeep was the architect of Sri Lanka's win against Afghanistan in Cardiff last week, claiming four wickets for 31 runs.
"Pradeep will not take part in Sri Lanka's game against Bangladesh on Tuesday, as he will need a week's time to recover from the injury," team manager Asantha De Mel said in a statement.
Sri Lanka have won one game, lost one and their last game against Pakistan was abandoned without a ball being bowled due to rain.
Bangladesh have lost two games and won one so far.
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(Reporting by Saikat Chatterjee; Editing by Toby Davis)
