The confrontation between the two sets of players -- in a match West Brom won 2-1 -- occurred when Watford's Roberto Pereyra was red-carded six minutes from time for lashing out at James McClean after the latter clattered into him.
"Both West Bromwich Albion and Watford have been charged for failing to ensure their players conducted themselves in an orderly fashion and/or refrained from provocative behaviour," read a statement from the FA.
"It follows an incident in the 84th minute of the game on Saturday December 3, 2016.
"Both clubs have until 6pm (1800GMT) December 8, 2016 to respond to the charge."
Earlier on Monday Manchester City and Chelsea had been brought to book by the FA and charged over the ugly scenes in the dying minutes of the London side's 3-1 win on Saturday.