Dave Watson's side - who beat local rivals Sunderland in the fifth round on Wednesday night - will entertain Tottenham Hotspur or Norwich City at St. James' Park.
Spurs and the Canaries meet at Stevenage's Lamex Stadium on Thursday, 2nd February. Quarter-final ties must be played by Saturday, 25th February.
When Newcastle last reached this stage in 2015, they played eventual winners Chelsea in front of 11,664 at St.James' Park.