He is one of two Rhinos players handed penalty notices following last week's defeat by Catalans Dragons, along with fellow forward Rhyse Martin.
Two Wakefield Trinity players have also been suspended, along with St Helens' Sione Mata'utia, who will be ruled out of this Saturday's Betfred Challenge Cup final against Castleford Tigers, unless the punishment is overruled on appeal.
Thompson was suspended for one game after being sent-off in Rhinos' win at Salford Red Devils two weeks ago and is now facing a three-match layoff.
The Rugby Football League's match review panel issued a three-game penalty notice after charging him with a grade C dangerous throw in the fourth minute of the game against Catalans last Friday.
Martin received a one-match suspension for grade B dangerous contact following an incident in the 71st minute.
Catalans' Joel Tomkins will miss Friday's rematch after receiving a two-match penalty notice for a grade B dangerous throw and teammate James Maloney was issued with a similar punishment for grade B dangerous contact.
Trinity's Joe Arundel and Ryan Hampshire were both handed a one-game penalty notice for grade B dangerous contact in last week's defeat by St Helens, ruling them out of the game at Salford Red Devils on Friday.
Saints' Mata'utia received separate one-match penalty notices for a grade B high tackle and dangerous contact.
He is now set to miss a Wembley showdown with his brother Peter, who plays for Cup final opponents Castleford.
Wigan Warriors' Jackson Hastings received a one-game penalty notice for grade A 'other contrary behaviour' against Huddersfield Giants, whose Joe Greenwood was banned for three matches over grade C dangerous contact.
Warnings went to St Helens' Tommy Makinson (other contrary behaviour) and Salford's Pauli Pauli (shoulder charge) .