The former Melbourne and Crusaders back rower was sent off just before half-time in last Thursday's Super League derby win at Warrington after catching Hodgson high and late in the face.
Cahill was charged by the Rugby Football League's match-review panel with a grade C reckless tackle and, after submitting an early guilty plea, will sit out the Vikings' final games of the season against Hull KR and Salford.
London Broncos forward Matt Cook has admitted punching during his side's 26-12 defeat by Huddersfield. He escapes a ban but will not be eligible to make another early guilty plea for 12 months.
Huddersfield forwards Ukuma Ta'ai and David Faiumu also submitted early guilty pleas to grade A punching charges arising from the same incident and avoid suspension.
Leeds hooker Paul McShane will miss his side's next game against Catalan Dragons after admitting a grade B offence of a dangerous lift during their defeat by Hull KR and accepting a one-match ban.