Jennings sustained the damage to his right hand during Ireland's 16-0 defeat against Argentina in the second Test of their summer tour.
The Leicester openside will undergo surgery tomorrow, forcing him to miss Ireland's training camp in Spala, and he is expected to be out for up to six weeks.
Crucially, he will also miss the World Cup warm-up clash with Scotland on August 11 - with head coach Eddie O'Sullivan set to unveil his final 30-man squad the following day.
The Murrayfield Test would have been his only opportunity to play his way into contention, amid fierce competition for places in Ireland's back row.
Jennings had a scan on the thumb last month which indicated a small amount of bruising with no break.
But upon the 25-year-old's return to pre-season training, the injury flared up again - and a repeat scan revealed a small fracture.
Following the operation, the thumb will be put in a cast for the duration of his recovery - and his participation in the Ireland's summer conditioning programme will be heavily restricted.