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.
His bail request on Sunday was denied, as was another application for release on Monday, according to a Sydney Downing Centre local court document, in a hearing closed to the public.
Gunathilaka appeared at the hearing via audio visual link from Surry Hills police station.
Meanwhile, Sri Lanka Cricket announced Gunathilaka, who has featured in eight Tests, 47 ODIs and 46 T20s, has been suspended from all forms of cricket with immediate effect.
The 31-year-old had been in Australia for the T20 World Cup and although he was ruled out of the tournament after playing one first-round match, he remained with the Sri Lanka squad.
An SLC statement said: "The Executive Committee of Sri Lanka Cricket decided to suspend national player Danushka Gunathilaka from all forms of cricket with immediate effect.
"(SLC) will not consider him for any selections after being informed that Mr Gunathilaka was arrested and charged with sexual assault of a woman in Australia.
"Furthermore, Sri Lanka Cricket will take the necessary steps to promptly carry out an inquiry into the alleged offense, and, upon conclusion of the aforementioned court case in Australia, steps will be taken to penalise the said player if found guilty.
"Sri Lanka Cricket wishes to emphasize that it adopts a 'zero tolerance' policy for any such conduct by a player and will provide all the required support to the Australian law enforcement authorities to carry out an impartial inquiry into the incident."
Sri Lanka were eliminated from the World Cup at the Super 12s stage, losing their final match against England at the SCG at the weekend.