The suspensions were announced by the competition organisers after a three-man foul play review committee studied the separate incidents.
Otago Highlanders winger Naholo was red-carded for a no-arms tackle on a Northern Bulls opponent during a match won 17-10 by the visitors in Pretoria.
Bulls lock Snyman got his marching orders soon after for storming into a ruck using only his shoulders.
Naholo misses the match against Australian side Western Force in Perth Saturday as Highlanders continue their pursuit of a quarter-finals place.
Snyman must watch from the stand when Bulls play Golden Lions in Johannesburg Saturday and Wellington Hurricanes of New Zealand in Pretoria next weekend.
Bulls, who are out of the running for a last-eight slot, do not play during the other two weeks of the ban.