Mr Buck has denied the charges
A retrial will be arranged for later in the year.
On Tuesday, before any evidence had been called, the jury of nine women and three men at Isleworth Crown Court in west London was told its services were no longer needed.
"Matters have arisen which necessitate that this trial cannot proceed at the moment," said Judge John Crocker.
"I can tell you no more I am afraid. I am discharging you from bringing in
verdicts in this case."
The 44-year-old musician was accused of assaulting British Airways cabin staff on his way to London on 21 April for a concert.
Mr Buck has denied being drunk on an aircraft last April.
He also denies two counts of common assault involving cabin services manager Mario Agius and stewardess Holly Ward, and one charge of damaging British Airways crockery.
Judge John Crocker adjourned Monday's hearing when the news of a passenger jet crashing near John F Kennedy airport outside New York reached the court.
US members of the court were allowed to make enquiries about friends and relatives before the trial resumed.
REM are widely regarded as one of the most influential groups of the past two decades and have been an inspiration for a generation of alternative rock bands.
The group formed in 1980 with a line-up of Michael Stipe, Peter Buck, Mike Mills and Bill Berry.
Yet, REM did not hit mainstream chart success until the release of their Green album in 1988.
Their albums have also included Murmur, Reckoning, Document, Out of Time and Automatic for the People.