Gunathilaka was arrested at the Sri Lanka team hotel in the early hours of Sunday morning and charged with four counts of sexual intercourse without consent following a police investigation.
The 31-year-old, who has played eight Tests, 47 ODIs and 46 T20s, remains in custody after twice being denied bail while Sri Lanka Cricket has suspended him from all forms of cricket.
The governing body has now announced the formation of a three-person panel to probe the incident, as well as other occurrences that are claimed to have happened during Sri Lanka's time in Australia.
Sri Lanka Cricket did not give details of the incidents that will be examined.
A statement said: "Sri Lanka Cricket wishes to announce the appointment of a three-member investigation panel consisting of Justice Sisira Ratnayake (Retired High Court Judge), Mr Niroshana Perera, attorney-at-law, and Mr Asela Rekawa, attorney-at-law, to initiate an inquiry into the alleged incident involving player Danushka Gunathilaka.
"The committee will also focus the inquiry on various alleged incidents that have come to the attention of Sri Lanka Cricket and that are said to have allegedly taken place during the national team's stay in Australia.
"The panel in this process will call for an immediate explanation from the team manager pertaining to his conduct, with references to the occurrence of such incidents.
"Upon submission of the said report by the panel, the executive committee of Sri Lanka Cricket will take stern disciplinary action against the players and or officials if proved any wrongdoing or negligence when carrying out official duties."
Gunathilaka played just one match at the World Cup before a tear to his left hamstring ruled him out of the rest of the tournament although he remained with the Sri Lanka squad.
Sri Lanka were eliminated at the Super 12s stage, losing their final match against England at the SCG at the weekend, and the rest of their contingent has since flown home.