The former Wigan and England back-rower was referred to a Rugby Football League operational rules tribunal after footage from last Friday’s play-off game against Leeds appeared to show him making contact with Myler’s backside.
Tomkins, who needs one more appearance to reach 300 in his career, was on Tuesday night found guilty of “other contrary behaviour” by the panel, which gave him the minimum sentence for a Grade F offence and fined him £500.
Along with hooker Michael McIlorum, who was banned for six matches for two offences in that game, he will miss the Dragons’ semi-final against St Helens on Friday and the Grand Final a week later if they get there.
The French club engaged Leeds-based sports lawyer Richard Cramer to represent them at the hearings, which began at 5pm and lasted until nearly midnight.
It is unclear whether the club will appeal the decisions.
Earlier, McIlorum admitted making a high tackle on Leeds hooker Brad Dwyer which earned him a one-match ban.
He challenged the severity of the grading but the tribunal upheld the Grade B charge and increased the ban to two matches and imposed a £500 fine.
The Ireland international was also charged with a Grade F charge of “other contrary behaviour” after lifting an injured Dwyer up off the ground and was facing a separate ban of eight matches or more.
McIlorum pleaded guilty to the charge but succeeded in having it reduced to D and the tribunal imposed a four-match suspension, with no fine.
The loss of their first-choice hooker, who has started all but two of his team’s 16 league and cup matches in 2020, will be keenly felt by the Dragons as they bid to reach their first Grand Final.
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