United Passions was funded by about £17m of Fifa cash, and was completed before corruption charges were made against 14 of its officials in May.
Starring Tim Roth as Sepp Blatter, the hagiography of football's governing body has had damning reviews.
The Village Voice called it "not merely ham-fisted, but pork-shouldered, bacon-wristed, and sausage-elbowed".
The Guardian added that "as proof of corporate insanity it is a valuable case study."
The movie's budget was estimated at between $25m - $32m (£16- £21m), with Fifa said to have put up about three-quarters of the money.
It debuted in the States on Friday, on just 10 screens.
According to The Hollywood Reporter, the FilmBar cinema in Phoenix reported takings of just $9, meaning only one person bought a ticket.
Its release came as Fifa faces an investigation into allegations of corruption during the bidding process to host the 2010 World Cup.
The US Department of Justice has indicted a total of 14 current and former Fifa officials and associates on charges of "rampant, systemic, and deep-rooted" corruption following a major inquiry by the Federal Bureau of Investigation (FBI).
President Sepp Blatter stood down last week, although he faces no charges himself.
United Passions purports to present the history of Fifa through three leaders, and co-stars Sam Neill as Blatter's predecessor, Joao Havelange, and Gerard Depardieu, who plays Fifa founder Jules Rimet.
Depardieu was the only actor who attended the film's world premiere at the Cannes Film Festival in 2014.
A vanity film about the history of Fifa has flopped in the US, taking just $607 (£397) in its opening weekend.