The 51-year-old was sent to the stands by the referee after clashing with Bolton Wanderers boss Phil Parkinson in their EFL Cup second-round clash at the Macron Stadium.
The incident occurred in the 88th minute following Barry Bannan's challenge on Filipe Morais during the game, which finished as a 3-2 win for Bolton.
Carvalhal was subsequently charged with misconduct by the FA and found guilty at an Independent Regulatory Commission hearing.
The manager has also been fined £4,000, while Parkinson has been fined £2,000 after admitting misconduct and accepted the standard penalty.
Wednesday sports scientist Andy Kalinins was also charged for misconduct following a 90th-minute incident in the same game, and will serve an immediate two-match touchline ban after admitting the charge, as well as being fined £3,000.