Television pictures appeared to show the Gunners midfielder, raising a finger towards the crowd during the 6-3 defeat by Manchester City.
The incident went unnoticed by match officials but was caught on video and assessed by the FA retrospectively.
The 21-year-old has until 18:00 GMT on Wednesday to respond to the charge.
Wilshere has previous form for abusive behaviour. Back in 2011, a taxi driver told how the Arsenal star spat at him and hurled abuse – because the cabbie had a Spurs hat on.
63 year old Brian Spence, said the £50,000-a-week England midfielder launched into a foul-mouthed rant after seeing the driver was a fan of his team’s North London rivals.
Wilshere, was on a boozy night out with three pals in London’s West End when he saw Brian standing by his cab outside Sophisticats lapdancing bar shortly after midnight.
Grandfather Brian said: “I had no idea who he was. He pointed to my cab and said, ‘You’re f***ing taking us’. When I told him he was too drunk he got even more aggressive.”
Brian of Gants Hill, North East London, got into his cab but Wilshere lurched towards the open window and spat, hitting the window.