Shannon secured their ninth AIB League Division One title on May 9 when they won the final at Thomond Park against Dublin side Clontarf after extra-time courtesy of scoring the first try of the game.
Commenting on the invitational challenge match, Finbarr Crowley, IRFU Domestic Game Chairman, said: "This game is a fitting reward for the AIB League champions in what was one of the most memorable finals in recent memory.
"The level of effort and commitment that was shown on the day is just a small percentage I am sure of what went into the entire season and this invitation to represent Ireland as the club champions is another accolade for Irish club rugby and the Shannon club.
"The Basque region has an incredible rugby history, sharing much of the same traditions that exists in our own clubs and hopefully this will be another opportunity for them to represent Irish club rugby with pride."
The Ireland Club XV, represented by Shannon, will take on Gernika RFC on Saturday, May 23 (kick-off 4pm (local time)).