The injury will see the 22-year-old miss his first match since joining the Giants for the 2012 season.
Giants' head of sports science John Quinn says Davis will be put on a restricted training program.
"Phil underwent scans and there was a fracture present so he'll be on a non-weight bearing training program for the next month due to the injury," said Quinn.
"We believe the injury was triggered by a knock to the lower back in recent weeks and it would continue to get worse if he played on."
Forward Setanta O'hAilpin will also miss Saturday's match against Essendon with a calf injury.
O'hAilpin, who has kicked eight goals in his first two games back from a knee injury is expected to return for the Giants in the round seven match against Adelaide at Skoda Stadium.
In better news for GWS, midfielder Dom Tyson remains on track for a return this month following pre-season knee surgery.
