The scratchy, black-and-white footage is from a match against Burnley at their Turf Moor ground on December 6, 1902.
It was made to be shown to workers at the Burnley Mechanics Institute that evening but the screening was cancelled because Burnley were defeated 2-0.
The film was then lost for nearly a century before being discovered in a barrel in the basement of a shop in Lancashire which was due to be demolished.
The demolition crew gave the film to a local historian who passed it to the British Film Institute (BFI). The BBC will broadcast the film on Friday, January 21.
The match at Burnley took place just months after United had assumed their now world-famous name. Until that year, they were known as Newton Heath.
The club, founded in 1878 by workers from the Lancashire and Yorkshire railway, had almost gone bankrupt the previous year before being saved by a rich local brewer.
They won the first of their 15 English league titles in 1908 and went on to become one of the most successful clubs in British soccer and the richest in the world.
