The young Blues will face local rivals Wexford Youths in the quarter-final match, which is due to take place on Saturday February 25th at the RSC.
The prize for the winners of the Southeast derby tie will be a home semi-final against either Cork City or Salthill Devon.
The full draw is as follows:
Quarter-Finals (to be played weekend of 25th/26th February)
A: Shamrock Rovers v Dundalk (Tallaght)
B: Waterford United v Wexford Youths (RSC)
C: Bohemians v Derry City (Dalymount Park)
D: Cork City v Salthill Devon (Bishopstown)
Semi-Finals (to be played weekend of 24/25th March)
Winners of C v Winners of A
Winners of B v Winners of D