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 case of a man accused of a homosexual rape in an Edinburgh graveyard has been deserted and will restart with a fresh jury.