"He has been reviewed by a specialist, who unfortunately confirmed that Jamie will need to spend the next four weeks in plaster," said Ospreys physiotherapist Chris Towers.
"That will be followed by a period of strengthening and rehabilitation. All in all we could be looking at an eight-week lay-off."
Nutbrown only arrived at the Liberty Stadium last week and his enforced absence means the Ospreys must now rely on Rhodri Wells and youngster Rhys Webb to fill the No9 shirt.
Nutbrown had been expected to play an important role for Sean Holley and Jonathan Humphreys' side, particularly while Wales international Mike Phillips continued to recover from a serious injury. Phillips is now likely to be back playing before the former New Zealand A man, as he hopes to return to action next month.