Jonathon Wilson, 43, is charged with attacking the Outlander and River City actor in March this year.
Mr Burn is said to have been assaulted in Crichton Close in Edinburgh's Holyrood area on 3 March.
The attempted murder charge claims the 60 year-old was repeatedly struck on the neck with a knife.
Wilson was not present for a hearing at the High Court in Glasgow today.
It was agreed between prosecutors and Wilson's legal team that he is not fit to stand trial.
An examination of facts hearing, which will look at the circumstances of the case, will instead take place in Edinburgh in December.
Mr Burn had finished speaking at a tribute to the late Scottish poet Tom Leonard at the Scottish Poetry Library in Edinburgh when he was allegedly assaulted outside the venue about 3:30pm.
The actor was initially treated in hospital, but later released.