It is cruel luck for Cullen who was hoping to add to his 19 Ireland caps, the last of which he gained on last summer's tour to Argentina.
Michael Cheika said: "Leo had a shoulder operation last week and he will be out for the next few months. It's a massive blow for him because he has been so consistent for us this season.
"He had put himself right up there for (Ireland) selection in what is one of the most competitives areas in the squad."
Cullen, who recently made his 100th appearance for Leinster, admitted prior to this year's Six Nations championship that he 'would love to be back involved with the Ireland squad in any form at this stage.'
The 30-year-old admitted: "When you are on the sidelines and looking in from the outside, you get a little bit jealous, especially because it has been such a successful period for Irish rugby (in recent years).
Meanwhile, Cheika has named Shane Horgan in his extended squad for Saturday's Magners League clash with the Newport Gwent Dragons.
Having recovered from a short illness, the Ireland winger will be hoping for some game-time over the next two weekends ahead of Ireland's pre-tour encounter with the Barbarians on May 27.
Horgan's international colleague Gordon D'Arcy is still out with an arm injury and it is uncertain whether he will play in Leinster's final game of the season against the Dragons on Friday week.