The Italian loosehead faced a disciplinary hearing in Neath on Wedesday via video conference.
Rizzo was sent off in the 28-8 defeat by referee John Lacey after he cleared out Scarlets scrum-half Gareth Davies.
The Edinburgh forward contravened Law 10.4 (h): “A player must not charge into a ruck or maul. Charging includes any contact made without use of the arms, or without grasping a player.”
The all-Welsh Disciplinary Panel, comprising of chairman Simon Thomas, Rhian Williams and Richard Cole concluded that the player was guilty of reckless rather than intentional behaviour and therefore warranted a mid-range sanction point of six weeks.
In light of the off field mitigating circumstances, the panel applied mitigation of 40 per cent and reduced the ban to four weeks.
The player, who has the right to appeal, will be available to play again from Monday 23 October.
He will miss Edinburgh’s Guinness Pro14 matches again Leinster on Friday and Zebre on 6 October, and their opennig two European Challenge Cup ties, against London Irish and Krasny Yar.