Byrne, who turned 51, was over the moon when "X-Factor" mentor and judge Louis Walsh gave her the surprise.
Walsh called her on her birthday to give her her present.
"He (Walsh) was the one who broke the good news to her about the invitation," said a source.
"She couldn't believe it when he told her that Jon had invited her backstage at his Irish gig.
"She's a huge fan of his so it was the best present ever for her. It's really made Mary's week. The past few weeks on the programme have been hard but now she's really starting to enjoy all the perks that comes with her new-found fame."
Byrne, a checkout worker in a supermarket in Dublin, is down to the final ten of the competition and is one of the favorites to win the whole thing.
Bon Jovi will play two gigs in the RDS in Dublin in June 2011.
Earlier in the week Byrne revealed some information about this weeks show.
On the Derek Mooney RTE radio show Byrne said this week's song is a "new ballad, not an old ballad."
"It’s beautiful song and it’s very touching. That’s all I can say. If I can put it across the way I put across my old ballads the whole of Ireland and myself will be crying."
When another guest on the show guessed the Faith Hill song, Byrne said "Yes."
And Byrne admitted another little secret.
She said, "I feel fantastic. I really do. I’ve been losing weight. I’ve lost nearly a whole dress size."
Her 23-year-old daughter is scheduled to fly to see her mom perform live this week on the show.