Girvan Dempsey's Leinster A team, who had six straight wins to top Pool 1, qualified as top seeds to earn the home quarter-final.
The sides met at the semi-final stage of the competition in the last two seasons with Leinster A prevailing last year before going on to win the competition.
Munster A beat Leinster A in the semi-final in 2012 before also going on to win the B&I Cup.
Commenting on the draw, Munster A Head Coach Peter Malone said:
"It's a big opportunity, there's a great history at all levels between Munster and Leinster but at 'A' level we've played each other in the semi-final in the last two years and it's one-all. Leinster are one of the leading teams in the competition so we're really looking forward to it.
"I haven't seen them this year but I'm sure they'll have a style similar to the senior team. We'll try to get a video or two of them to watch before we play them, but we know how to expect Leinster to play. They're physical, they work hard at the breakdown and we've got to match that and really be up for it."