The former New Zealand international was sent off in the 33rd minute of Saints' 26-18 fourth-round defeat at Craven Park for a high tackle on Craig Hall.
He was subsequently charged with a Grade E offence and received the minimum four-game suspension and a £300 fine when he appeared in front of the Rugby Football League's disciplinary committee in Leeds.
Meli was already facing a lengthy spell on the sidelines after dislocating his elbow in the tackle which caused a whiplash injury to his opponent.
St Helens will also be without makeshift scrum-half Jon Wilkin and winger Ade Gardner through suspension for Saturday's Super League game at London Broncos.
The players both submitted early-guilty pleas after being placed on report for late tackles in the Cup-tie.
Wilkin, one of only two Saints players to have started all 13 league and cup games so far this year, was banned for two games for a Grade C dangerous shoulder charge on Michael Dobson while Gardner was given a one-match ban for a similar offence on Kris Welham.
Catalan Dragons hooker Ian Henderson has been cleared to face Huddersfield at the Stade Gilbert Brutus on Saturday after being found not guilty of striking.
Henderson was sent off during his side's 50-12 fourth-round Cup win at Hunslet on Sunday and charged with a Grade B reckless strike.
He was eligible to submit an early-guilty plea but the club contested the charge at a hearing via Skype and he was found not guilty.