Wickham, 22, appeared to elbow Belgian defender Vertonghen in the face during a tussle at a second-half corner.
Vertonghen, whose team won 3-1, was substituted after the incident, which was missed by referee Martin Atkinson.
Wickham has until 18:00 GMT on Tuesday, January 26 to respond to the charge.
Crystal Palace striker Connor Wickham has been charged with violent conduct by the Football Association after his clash with Tottenham defender Jan Vertonghen on Saturday.