Bowling all-rounder Dushan Hemantha has been named as his replacement in the squad.
The injury is a serious blow for the co-hosts, particularly after Hasaranga made a promising start to the World Cup by claiming three wickets in Sri Lanka's 20-run victory over Ireland in their opening match.
His absence robs Sri Lanka of one of the world's premier T20 spinners. The 28-year-old sits fifth on the all-time list of most T20 international wickets with 154.
Sri Lanka fast bowler Eshan Malinga was ruled out of the tournament after dislocating his shoulder, with Pramod Madushan brought in as his replacement.
The co-hosts face Oman in their second Group B game on Thursday.