The band will play an intimate set in support of their third studio album Scars & Stories, which will be released in the UK on March 5.
The concert is part of The Absolute Radio Sessions, with tickets available to win by tuning into the station or visiting its official homepage.
Speaking about the gig, Absolute Radio presenter Polly James said: "The Fray are a really top band. I remember the first time I heard 'How to Save A Life' and I've been a fan ever since.
"We're in for a real treat at the Hard Rock Cafe - The guys are truly talented, they all play multiple instruments and I can't wait to hear their new material."
A further 20 complimentary tickets are available for members of the public and can be won by 'liking' the post about the gig on The Back Room Facebook page.
Highlights from the show will air on March 8 from 8pm on Absolute Radio.
Watch the music video for The Fray's latest single 'Heartbeat' below: