Jennings won't feature in the tournament opener at the Liberty Stadium in just over a fortnight's time after suffering a hand injury in last Friday's domestic defeat to Glasgow Warriors at Scotstoun.
The 32-year-old former Leicester Tigers forward fractured a bone in his right hand and the Leinster staff say he will miss 'the next few weeks' of action.
That length of absence is set to rule Jennings out of the home tie with French Champions Castres Olympique a week later as well but he should be back in action in time for the mouth-watering double header with Northampton Saints on December 7 and 14.
There is plenty of good news on the injury and fitness front for Leinster fans, though, with a host of stars either ready or close to a return to the team.
Lions tourists Brian O'Driscoll and Jamie Heaslip are hopeful of featuring for the first time this season when Leinster welcome Cardiff Blues to the RDS on Friday, a week after fellow Lions Cian Healy and Rob Kearney were involved in Scotland.
O'Driscoll and Heaslip both took part in a two-day Ireland training camp earlier this week and are pushing for a first appearance of any sort since the Lions lost the second Test to Australia in Melbourne on June 29.
Australian cross-code international Lote Tuqiri's hamstring strain isn't as serious as it could have been and he could be involved against the Blues.
Former Ireland back and 2009 Lion Luke Fitzgerald is making good progress from the groin / pelvic problem he suffered against the Scarlets on September 6 and, although he isn't expected to play this week, he could return in time to face the Ospreys.
Sean O'Brien is also on the mend following arm surgery after his adventures with the Lions and is another hoping to be involved when the Heineken Cup kicks off, while Quinn Roux is heading in the right direction and Darragh Fanning will be available this week having recovered from the training knock that stopped him from being involved against Glasgow.