Relegated Villa were leading 2-1 at Vicarage Road before two late goals from Watford captain Troy Deeney.
Ayew and team-mate Idrissa Gana Gueye were then allegedly involved in an incident involving home supporters.
Reports suggest the Ghana international, 24, climbed over advertising boards to confront fans.
Ayew, who was substituted in the 79th minute, is believed to have taken exception to something said in the Sir Elton John Stand.
His low drive had earlier restored Villa's lead, but Aly Cissokho was sent off with 17 minutes to play and Watford mounted a late comeback.
The Football Association says it will investigate striker Jordan Ayew's actions during Aston Villa's 3-2 defeat at Watford on Saturday.