Hasaranga suffered the injury during Sri Lanka's victory against Ireland in Colombo on Sunday, and a subsequent MRI scan revealed a serious tear to the left hamstring.
The wrist-spinner still completed his spell against the Irish, taking 3-25 in his four overs as Sri Lanka kicked off their global tournament with a 20-run win.
Hasaranga will now miss further group matches against against Oman on February 12 in Pallekele, followed by Australia on February 16 in Pallekele, and finally Zimbabwe in Colombo (RPS) on February 19.
The ICC have yet to approve a replacement player to join the Sri Lanka squad.
Tim Seifert and Finn Allen produced a record-breaking opening stand as New Zealand cruised to a 10-wicket victory over the United Arab Emirates in their T20 World Cup Group D clash in Chennai on Tuesday.
Bas de Leede delivered a brilliant all-round performance as the Netherlands claimed their first points of the T20 World Cup, defeating Namibia by seven wickets.
The Pakistan government has given it's approval for their national team to take the field and play India in their T20 World Cup encounter, scheduled for Colombo on 15 February.
The International Cricket Council (ICC) has concluded that Bangladesh will not be sanctioned for refusing to play T20 World Cup matches in India.
