كتب : Omar AbdelAziz
The Spain international was subjected to a challenge by two opposition players in the 3-0 defeat, where he had to be stretchered off in the 65th minute.
"I am very sad because a beautiful part of the season is approaching and I'll miss it," said Cazorla said.
"It's a big disappointment for me. I understand the severity of the injury and I will continue to support my team-mates. I fell badly and as soon as I heard a crack I knew that something was wrong."
Cazorla, who has been influential to Villarreal's season so far, will miss Wednesday's Champions League clash with Arsenal.
The 24-year-old, who is also a regular for Spain, is ruled out of the European champions' FIFA Confederations Cup in South Africa this summer.
Although his absence for the rest of the season was confirmed, further tests will be conducted to determine the exact period of his layoff.