Rachid Lamrabet, 42, who lives in London, denies sexually assaulting a 25-year-old man at Greyfriars Kirk, on 26 August 2015.
The judge said the case was being deserted after a matter arose and he heard legal submissions.
He added that there were "good reasons" for the move.
The trial had only just begun at the High Court in Livingston on Monday.
Dismissing the jury members, judge Lord Woolman told them: "In the light of submissions made to me I regret that I'm going to discharge you as a jury and continue this case until tomorrow.
"I'm not in a position to tell you the exact reasons for that all I can tell you is that there are very good reasons.
"I very much regret that this has happened, but sometimes matters occur which are outwith our control.
"I regret and I'm sorry for any inconvenience caused to you."
Mr Lamrabet, is accused of engaging in consensual sexual activity with his alleged victim but ignored him when he was told to stop.
The charge states that he seized the younger man by the body, pushed him to the ground and raped him to his injury.
English is not the accused's native language, and a Spanish interpreter sat with him in the dock so he could understand the proceedings.

The museum closed last October to allow work to upgrade the building and provide more display space.
About half of the project's £66m cost is being funded by the council.
In April 2015, the council provided £5.7m to kick-start the building's revamp, which houses treasures donated to the city by collector Sir William Burrell in 1944.
The Burrell collection consists of more than 8,000 artefacts but fewer than a fifth of them have been on show at any one time.
When it re-opens to visitors in 2020, the basement of the building will become part of the exhibition space, so that 90% of the objects can be viewed by the public.
The Heritage Lottery Fund has given £15m to the project and the UK government has also contributed £5m.
It is hoped a fundraising campaign will raise the rest.
Cllr Archie Graham said: "Sir William's great legacy has been described as the greatest gift a city has ever received and we have a moral duty to ensure it is housed in the finest of buildings."

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13 May 2015 Last updated at 12:41 BST
The Haka means "fierce dance" and was traditionally performed by the Maoris before going into battle.
Nowadays the Haka is performed during special ceremonies.
The New Zealand rugby team also perform the special dance before all their international matches.
Prince Harry is currently on a week-long tour of New Zealand.
The case of a man accused of a homosexual rape in an Edinburgh graveyard has been deserted and will restart with a fresh jury.
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A further £27m for the refurbishment of the Burrell Collection has been approved by Glasgow City Council.
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Prince Harry has taken part in a traditional Maori Haka during his tour of New Zealand.