The Grecians' Under-21s caused an upset earlier this evening when they beat their Crystal Palace counterparts 3-2 at Selhurst Park in Qualifying Round 2.
Exeter, who have a Category 3 academy, previously saw off Torquay United in Qualifying Round 1 and now move into the first round proper.
Saints are one of 19 Category 1 clubs who begin their involvement in the Round of 32 stage of the competition, which is in its inaugural year.
The tie is due to be played within 14 days of Monday 18th November 2013, with a confirmed date to be announced in due course.
The Round of 16 will be the first stage at which the Under-21 Premier League Cup will be contested on a national basis. The final will be played over two legs, which are home and away at the main stadia of both teams.
Meanwhile, Saints' upcoming Barclays Under-21 Premier League game against Wolverhampton Wanderers has been postponed.
The match was due to take place on Monday 4th November at Staplewood, but will now be rearranged with a new date to be confirmed on saintsfc.co.uk