The All-Pro sustained the injury in the Patriots' win over the Atlanta Falcons on Sunday and underwent surgery on Tuesday to repair the damage, which will leave out of action for the rest of the 2013 campaign.
Wilfork said in a statement: "I just want to thank everyone for your support and encouragement. One thing I know is I signed up to play football. I don't regret anything that has happened and there is no need to feel sorry about it.
"I've been blessed to only have had one surgery prior to today and that was in high school. I know what signing up to play football means and I know the rewards and risks.
"I have so much confidence in our team and know that they will do great and I will be right besides them, maybe not in uniform but in all other ways. Thanks again."
The Patriots are 4-0 in their season after week four.