The Magpies, who beat Bournemouth 1-0 on Tuesday night to book their place in the last eight of the competition, were handed a home draw against the Foxes - who Newcastle play in the Premier League at the King Power Stadium on Boxing Day - in Thursday night's draw at the Etihad Stadium.
Former United goalkeeper Shay Given conducted the draw along with England stopper Mary Earps.
All quarter-finals will be played during the week beginning Monday, 9th January 2023, with two of the ties set to be broadcast live on Sky Sports.
Further details, including a confirmed date and ticket news, will be announced in due course.