The defender was shown a straight red card in the 25th minute after tangling with Hornets striker Troy Deeney.
Berra appeared to be holding back Deeney as he burst through on goal, and he was dismissed for "denying an obvious goalscoring opportunity".
Deeney went on to fire the winner in the 68th minute as Wolves left Vicarage Road empty-handed, and they will now contest Graham Scott's decision to send off Berra.
A statement from Wolves read: "Wolves will be submitting both written and video evidence to support their claim.
"A decision will then be received this week in advance of Saturday's fixture against Nottingham Forest, which Berra is currently due to miss as a result of his one-game suspension."
Wolves boss Stale Solbakken was enraged by the decision, and he said after the game: "I think I agree with everyone who say it's a very harsh one.
"There's no appeals from anyone, from a Watford player or even the dugout, and I think the referee just created a problem for himself after that."