Mac Allister's home debut for his new club ended after 58 minutes when referee Thomas Bramall sent him off for a high tackle on Ryan Christie.
Liverpool were leading 2-1 at the time and went on to complete a 3-1 victory at full time.
Liverpool manager Jurgen Klopp was unhappy with the referee's decision to dismiss Mac Allister and the club launched an appeal.
An independent regulatory commission looked into the case and have decided to overturn the referee's decision.
Mac Allister was expected to miss three games through suspension but will now be available to face Newcastle United, Aston Villa and Wolverhampton Wanderers.
“An independent regulatory commission has removed Alexis Mac Allister’s three-match suspension following a claim of wrongful dismissal,” read a statement posted on the FA Spokesperson account on Twitter.
“The Liverpool midfielder was sent off for serious foul play during their Premier League game against Bournemouth on Saturday, 19 August.”
Liverpool responded to the FA decision by saying: “A club appeal against the suspension has now been upheld by an independent regulatory commission, meaning Mac Allister is eligible for selection when the Reds travel to Newcastle United on Sunday.”
Mac Allister, who won the FIFA World Cup with Argentina last December, joined Liverpool from Brighton and Hove Albion this summer.
