The melee was sparked by Pedro’s late sliding challenge on Jefferson Lerma. Wilshere and Pedro were both given their marching orders by Tony Harrington after receiving second yellow cards.
A FA statement said: “AFC Bournemouth and Watford FC have both been charged with a breach of FA Rule E20 following their EFL Championship fixture on Saturday 27th February.
“Both clubs allegedly failed to ensure that their players and/or club officials conducted themselves in an orderly fashion during the 96th minute of the fixture and they have until Friday 5th March to provide their responses.”
Bournemouth winger Arnaut Danjuma scored the only goal in the 61st minute.
The Cherries are sixth in the table, eight points behind fellow promotion hopefuls Watford, who are third.
Additional reporting by PA.