Girvan Dempsey's Leinster 'A' team, who had six straight wins to top Pool 1, will be at home to Munster 'A' in a mouth-watering quarter-final clash.
Peter Malone's Munster 'A' side earned one of the best runners-up spots in the pool stages, finishing second behind Plymouth Albion in Pool 4 thanks to two closing bonus point victories.
Commenting on the draw, Malone said: "It's a big opportunity, there's a great history at all levels betwen Leinster and Munster 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."
The provinces are both former champions - Munster 'A' were runners-up in 2010 and lifted the trophy two years later, while Leinster 'A' were extra-time winners over Newcastle Falcons in last year's final.
Two more past winners, Bristol (2011) and Cornish Pirates (2010), will have home advantage in their quarter-final ties in April.
Whoever comes through the Irish interprovincial derby will be away to either Cornish Pirates or Pontypridd - both pool winners - at the semi-final stage in May.
BRITISH & IRISH CUP QUARTER-FINALS:
Match 1: Bristol v Rotherham Titans
Match 2: LEINSTER 'A' v MUNSTER 'A'
Match 3: Cornish Pirates v Pontypridd
Match 4: Leeds Carnegie v Plymouth Albion
- Matches to be played on April 4/5/6
BRITISH & IRISH CUP SEMI-FINALS:
Winners of Match 3 v Winners of Match 2
Winners of Match 1 v Winners of Match 4
- Matches to be played on May 2/3/4