The prognosis is that the injury will rule Wilkinson out until March, meaning he would miss England's Six Nations campaign.
He also faces a race against time to prove his fitness ahead of the British and Irish Lions tour to South Africa, which begins on 30 May.
Meanwhile, Bates said he welcomes the news that Falcons chairman Dave Thompson will be staying on in the role at Kingston Park.
Thompson, 63, had previously considered selling the club before decided to maintain control and Bates believes the stability his announcement proposes will be welcome.
"It does lift some uncertainty, I think that's a really important thing," he said.
"You've got to recognise Dave's contribution to rugby in the area and his continued support is a fantastic filip for the club.
"There has been a bit of uncertainty but that has been cleared up and I think we can move forward now."
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