The announcement was made by league sponsors Santander, who declared on Twitter: "We already have a winner of the #MVP September in @LaLiga.
"The chosen one is @ANSUFATI. CONGRATULATIONS, star!"
Fati only played one LaLiga match in September, as Barcelona began their season later than most due to their Champions League involvement last term.
However, the teenage forward made an instant impact when he scored twice in the first 20 minutes of a 4-0 win over Villarreal at Camp Nou.
He netted again, four days later, on October 1, in a 3-0 victory at Celta Vigo.
Fati has nevertheless been a revelation in recent weeks, becoming Spain's youngest lscorer in history at 17 years and 311 days old when he hit the third goal in a 4-0 win over Ukraine on September 6 in the Nations League.
Where superstar Messi has scored just once in three LaLiga games this season, Fati heads the scoring charts in coach Ronald Koeman's ranks.
Fati has played 203 league minutes so far and gobbled up the one opportunity defined by Opta as a 'big chance', after missing six of seven such openings last season.
Koeman has trusted him with starts in each game, while he only played from the first minute in 11 games during the 2019-20 LaLiga campaign, when he scored seven times.