The Magpies are one of 16 Premier League and Championship clubs invited to enter an under-21 side into the competition, and last week they were drawn alongside Doncaster Rovers, Notts County and Grimsby Town.
United will travel to Doncaster on Tuesday, 4th September (kick-off 7pm BST) and Notts County - managed by former Newcastle favourite Kevin Nolan - on Tuesday, 9th October (kick-off 7.45pm BST).
Doncaster have yet to announce ticket details but Notts County have confirmed that ticket prices will be £5 for adults, 65+, under-18s and under-16s.
Supporters under the age of 12 can gain admission for £1 if they are accompanied by an adult while accompanied under-sevens will be admitted for free.
All adult ticket prices will rise by £2 on the day of the game.
Newcastle will then face Grimsby at Blundell Park on Tuesday, 13th November (kick-off 7.45pm GMT).