Chris Hogg's side were due to face the Shrews on the week commencing 7th September but will now make the long trip to New Meadow on Tuesday, 22nd September, with kick-off taking place at 5.30pm (BST).
United's youngsters also face away trips to Crewe Alexandra and Bolton Wanderers in Group C of the tournament's Northern Section.
The Magpies, one of eleven Category One Academies competing in this term's competition, have played both Crewe and Shrewsbury since making their debut in the competition back in 2017/18.
Shrewsbury prevailed in a 3-0 triumph back in October, with goals from Fejiri Okenabrhie, Jason Cummings and Dave Edwards sealing maximum points for the League One outfit.
Newcastle were victorious in their last outing at Crewe, securing a 2-1 victory in the 2017/18 edition, courtesy of goals from Liam Smith and Luke Charman.
Newcastle enjoyed an impressive run to the Northern Section quarter-finals two seasons ago, which included a 100 per cent win ratio in Group G before eventually losing out to Sunderland at the Stadium of Light.