Former Red Shelvey clashed with the German midfeilder in the Jacks’ 4-1 Premier League defeat at Anfield on Monday night.
He appeared to fling back an arm into the face of Can, but the incident went unpunished at the time with referee Andre Marriner waving play on.
However, the FA have retrospectively punished Shelvey after reviewing the footage.
“Swansea City’s Jonjo Shelvey on Tuesday has been charged by The FA for violent conduct, following an incident in his side’s fixture with Liverpool,” said an FA statement.
“The incident, which was not seen by the match officials but caught on video, occurred during the fixture between the two sides at Anfield on Monday 29 December 2014.
However, he was quick to protest his innocence on Twitter after the Anfield game.
He tweeted: “Just wanna say I didn’t intentionally elbow Emre Can – I was just trying to get my arm across to get round him. It’s come off as if I’m trying to hurt another player and I can assure you that isn’t the case. And I apologised to Emre Can for catching him.”
“Shelvey has until 6pm on Wednesday 31 December 2014 to respond to the charge.”
Swansea manager Garry Monk said on Tuesday he does not believe Shelvey deserves disciplinary action for the incident, but if found guilty the 22-year-old, who was sent off at Everton at the start of November, could face a four-match ban, starting at QPR on New Year’s Day.
Liverpool forward Raheem Sterling, meanwhile, will not face retrospective action for pushing Swansea defender Federico Fernandez in the face after tangling with the Argentinian defender in the closing stages of the same game.
The FA confirmed that the incident was seen by at least one of the match officials at Anfield so no further action would be taken.