Alli, the PFA's Young Player of the Year, swung his arm at the West Brom midfielder during the first half of the 1-1 draw that left Tottenham's fading title hopes in tatters.
The incident was missed by the match officials, but the Football Association decided to charge England international Alli after reviewing video evidence.
"Dele Alli has been charged for an alleged act of violent conduct which was not seen by the match officials but caught on video," the FA said in a statement on Tuesday. He has until Wednesday to respond.
A three-match ban, the standard punishment for violent conduct, would rule Alli out of second-placed Tottenham's final games of the season.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
(Reporting by Toby Davis; editing by Ken Ferris)
