The draw was screened on Made In Tyne & Wear's Football Matters show on Thursday evening, with Peter Beardsley's side handed a tough trip to the Daren Persson Stadium.
North Shields, nicknamed the Robins, are currently top of the Ebac Northern League Division One. A date for the fixture has yet to be confirmed but will be announced on nufc.co.uk in due course.
United beat Morpeth Town 3-2 in the last eight earlier this month, with Callum Roberts, Tom Heardman and Dan Ward on target for the Magpies.
Blyth Town and Blyth Spartans will meet in the other semi-final.