The 27-year-old, who recently agreed a new deal at the club, suffered the injury during a pre-season friendly against MK Dons.
"It was absolutely ridiculous," Clark told the club's official website. "It was so innocuous, it was 10 seconds from the end of the game as well, which is the frustrating thing.
"To have five separate fractures in the same sort of area is tough. We're hoping for the best. He sees a specialist this week who will decide whether he needs an operation or not."
If an operation is needed, then Spector is likely to miss the start of the season.