He was stretchered from the pitch in considerable discomfort and taken to hospital where an X-ray revealed he had incurred soft tissue damage rather than a break.
Wasps are reluctant to set a date for his return and the 34-year-old will almost certainly miss the start of the Six Nations.
A club statement said: "Shaw will undergo review and treatment on his injury throughout this week.
"Further updates as to the extent of his injury will be issued by Wasps later this week."
Wasps initially feared the worst when Shaw went down beneath a pile of bodies and he required treatment on the pitch for five minutes before being carried off.
But subsequent scan results delivered encouraging news on the severity of the injury.
A spokesperson added: "Obviously it is good news there was no break to the ankle but he's still in discomfort and will be out for several weeks."
England open their Six Nations campaign against Wales on February 2 before travelling to Italy a week later and it is unlikely Shaw will feature in either match.