Simpson-Daniel fell awkwardly during Gloucester's pre-season defeat to Llanelli on Saturday and was undergoing surgery at the Winfield Hospital on Tuesday.
It remains unclear at present exactly how long Simpson-Daniel will be sidelined for - but he faces a race against time to feature for England in November.
It is another massive blow for the injury-jinxed 24-year-old, who had only just recovered from the haematoma that left him hospitalised on England's summer tour of Australia.
Gloucester head coach Dean Ryan said: "It is obviously devastating news and he will have our total backing.
"We will be supporting him in every possible way to ensure a quick recovery."
Simpson-Daniel has been limited to just nine caps in the four years since making his England debut because of glandular fever, back, shoulder and ankle injuries.