Sissoko caught fellow midfielder Arter during the second half at Bournemouth's Dean Court ground but escaped immediate sanction.
A Football Association statement on Monday said that as the incident was not seen at the time by referee Craig Pawson or his linesmen, Sissoko had been charged with violent conduct.
Spurs have until 6:00 pm (1700 GMT) on Tuesday to respond to the charge, but manager Mauricio Pochettino indicated they would not contest it.
"We accept that. We have reviewed the video," said Pochettino, ahead of Tottenham's visit to Liverpool in the fourth round of the EFL Cup on Tuesday.
"After the game it was difficult when I was asked about the action," the Argentine added. "It was true that it was difficult for me to appreciate the situation of what happened.
"But when I saw it on TV I need to say there was no intention but the elbow was in the face of Arter, that's clear.
"We accept the charge and now we need to move forward and expect a three-match ban."
Arter responded angrily in the immediate aftermath of the challenge, as players from both sides became involved in a scuffle, but he said afterwards: "He caught me straight in the face and if you get hit in the face anyone would have a reaction
"After the game he apologised. I'm not one to hold grudges. He said sorry, he didn't mean (to do) it, so that's the end of it.
"It looks like he elbowed me but he apologised and said it was an accident, so that's good to me."
