The 27-year-old received the diagnosis on Wednesday morning after undergoing a scan on an injury he picked up without any external intervention.
He was carried off the field in the 31st minute of the 2-0 win and now faces a lengthy spell on the sidelines.
"I felt immediately that something was not right with my knee, and it turned very painful very quickly," the Portugal international said on his club's official website.
"Now I can only hope that the operation goes well.
"It's going to be a hard time for me, but I know that my family, my team-mates and our fans are standing behind me and they will give me the strength I need to come through my recovery."
The loss of Vieirinha is a blow to the Wolves, whose director of sport Klaus Allofs said: "It's very bitter for Vieirinha and for us.
"We hope that he returns to fitness as quickly as possible and we will do all we can for him to make an optimal recovery."