The 29-year-old was seen to be making the hand signal towards the supporters when he was substituted
The Southampton striker was seen making the hand signal towards supporters when he was substituted during the match at the St Mary’s on December 30.
Austin will now not feature in Saturday’s Premier League match at Leicester City and he will also miss the home FA Cup replay with Derby County on January 16.
He will next be available for the Saints’ home league game against Everton on Saturday, 19 January.
An FA statement read: “The striker admitted his gesture in or around the 68th minute of the game against Manchester City on 30 December 2018 was abusive and/or insulting.”
The suspension will be a blow for Southampton as they are desperate for points.
The side currently sit 18th in the Premier League, two points behind Cardiff City in 17th.
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The 29-year-old has struggled for goals this season and has just three in 18 appearances in all competitions.