The draw - which was split into north and south sections - was made on Wednesday evening, following the conclusion of Leyton Orient's first-round clash with Queens Park Rangers, and the Magpies were handed an all-Premier League clash with the Clarets.
Newcastle have never met Burnley in this competition, but have faced them in the FA Cup - in 1894/95, 1953/54 and 1973/74. United came out on top in each tie, although required a replay in 1953/1954.
Steve Bruce's side reached the quarter-final stage of the competition last term, knocking out Blackburn Rovers, Morecambe and Newport County, but were beaten by Brentford in the last eight.
The tie will be played in the week commencing Monday, 23rd August. Confirmation of the date, and ticket news, will be announced on nufc.co.uk soon.