The game is part of a three-match Baa-baas tour which also sees them tackling Belgium in Brussels three days earlier and England at Twickenham on June 1.
The Ireland fixture takes place on Tuesday, May 27 at Kingsholm.
There had been speculation suggesting Chelsea's Stamford Bridge ground would have staged the match, which will serve as a warm-up for Ireland prior to their summer tour of New Zealand and Australia.
Barbarians president Micky Steele-Bodger said: "This is a new departure for us, but a very interesting one.
"Ireland were keen to add a fixture in Europe to their own summer tour before travelling on to New Zealand and Australia.
"With Lansdowne Road and Thomond Park still under redevelopment, we are playing at one of the traditional hotbeds of rugby union in the west of England.
"Kingsholm was an obvious choice, and one that we are sure will prove to be a great success for both players and fans."
The Barbarians have played Ireland on two previous occasions in 1996 and 2000, and they will be defending an unbeaten record against them.