Wales expect Hook to be sidelined for two to three weeks, leaving him facing a race against time to be fit for a potential quarter final against Ireland on October 8.
There are also concerns surrounding inform blindside flanker Dan Lydiate who turned his ankle in the opening moments on Sunday.
Lydiate faces a scan today and more will be known then on how serious the damage is.
"I think it's a grade one or two injury that James has," said Wales and Lions assistant coach Shaun Edwards.
"That usually means two or three weeks.
"Dan has to go for a scan on Monday. We're still in the dark about Dan, we'll know more after his scan.
"James' is a little easier detect to what it is. He has done his AC joint."
Former skipper Ryan Jones could be available for the fixture against Namibia after his recovery from a calf injury appeared to be progressing quicker than expected.
Jones was at first thought to be targeting the Fiji game as a likely return date but could be ready for action a week earlier.