The 31-year-old, who is in Australia for the T20 World Cup, was arrested at his Sydney CBD hotel in the early hours of Sunday and was refused bail by a court later in the day.
The left-handed batsman made a second application for release on Monday.
Magistrate Robert Williams noted Gunathilaka had no criminal history, but the application for release was later refused.
Outside court, his defence lawyer Ananda Amaranath called the decision "disappointing" adding his client was considering appealing the decision to the Supreme Court.
The bail application was made in a closed court, after the police prosecutor lodged an application to suppress the facts of the case and the indictment against the 31-year-old.
The motion to suppress was opposed by Mr Amaranath and Stephen Coombs, senior legal counsel for Nationwide News.
The pair made similar arguments - that the victim's name was already unable to be made public, and further suppression orders flew in the face of open justice.
Mr Williams granted an interim order closing the court on Monday - noting the court could grant an interim version of the request without considering its merits.
The order will be reconsidered on Wednesday.
The cricketer has been charged with four counts of sexual intercourse without consent.
He spent a night in custody in at Surry Hills Police Station before appearing in handcuffs and a grey T-shirt via video link at the Downing Centre Local Court on Monday.
"Yes sir," he told the court when asked if his video link was working.
Gunathilaka travelled to Australia with Sri Lanka's T20 World Cup team but only played in the team's first game, a loss against Namibia, before being ruled out of the competition with a hamstring tear.
The Sri Lankan man had been holding up well in police custody, his lawyer told media outside court.
"He has the full support of the Sri Lankan High Commissioner and the Sri Lankan Cricket Board. So he is OK," Mr Amaranath said.
Sri Lanka bowed out of the T20 tournament on Saturday night after losing their final match to England.
He has played nearly 100 T20 and one-day internationals for Sri Lanka as well as a handful of tests.
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