"I always pride myself on being relaxed, being cool with whoever I meet," Murray told The Early Edition's Rick Cluff, in the studio to talk about the band's upcoming show in Vancouver on Tuesday.
The Canadian operatic pop group has performed with stars like Sir Paul McCartney, Neil Young and Celine Dion.
Murray said he has always managed to keep his cool — with one exception.
The singer was playing golf in Mexico on his birthday when, at the ninth hole, he ran into George Clooney.
"He was sitting there eating fajitas and he walked up to us because he had seen our show last night."
Murray is a big fan of Clooney's work, and found himself at a total loss for words.
"I was completely tongue twisted, and all I could say was...I'd look at the ocean and go 'Break neck wave, break neck wave.'"
It was fellow member of The Tenors, Fraser Walters, who got him out of the situation.
"He taps me on the shoulder and is like, 'I got this one Clif.'"
Murray's still not sure why he lost his composure around Clooney.
"I think it was the fact that I was caught off guard on my birthday, after a few drinks, that might have been part of it."
To hear more from The Tenors' Clifton Murray on The Early Edition, click on the audio clip labelled: Canadian Tenor Clifton Murray.