It is the second ACL rupture the 22-year-old has sustained in his short career.
Laybutt's absence will be a blow to the Cowboys, who share the competition lead, after he had started the season with three tries in four games and appeared set to be a regular after veteran Peta Hiku left the club at the end of last season.
The Cowboys feared the worst after their 35-22 win over the Titans on Sunday.
"It is devastating news for the kid," coach Todd Payten said.
"Zac has put in a really good pre-season, got himself super fit and done some really good things for us in the first five weeks of the competition.
"He's been through it before. He had an ACL on the other knee many years ago, so he knows what is ahead of him."
The Cowboys do have depth in the position, and Payten said it would provide an opportunity for Semi Valemei, Tom Chester or Viliami Vailea.
"We will make a decision during the week based on what I have seen in the past month," Payten said.
In other injury news, Dolphins second-rower Felise Kaufusi will start rehabilitation on a hamstring strain on Tuesday in a quest to be fit for the "Battle of Brisbane'' with the Broncos on Friday night.
The veteran was rated long odds of being fit for the clash after leaving the field in the 26-16 win over the Wests Tigers, but has not given up hope of an unlikely recovery.
"Felise's chances of playing will depend largely on how he goes with his rehabilitation this week," Dolphins performance chief Jeremy Hickmans said.
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