Williams suffered the injury during training at the Blues' pre-season camp in Queensland on Friday and scans have confirmed a ruptured anterior cruciate ligament.
The 28-year-old will undergo surgery in the next few days before starting his rehabilitation.
"These incidents are so unfortunate and we are all feeling for Zac," Carlton football boss Brad Lloyd said.
"He could not have done any more this pre-season to get himself ready for the year.
"He will undergo surgery to repair his ACL and from there we will put a rehabilitation program in place for him over the next 12 months."
Williams signed a six-year contract with Carlton in a high-profile move from GWS but has managed just 23 games in two seasons in navy blue to date.
A calf injury limited him to just one game after round nine last year.
"He has had more than his fair share of bad luck with injury, Zac," Lloyd said.
"But in that time he has built up a lot of resilience, which he will no doubt tap into as we all support him on his road to recovery from here."
Williams was poised to join Adam Saad at half-back this year, with the pair capable of providing plenty of run out of the back half.
Williams' latest setback hurts Carlton's chances of ending a nine-year finals drought after they missed out by the barest of margins last season - their first under Michael Voss.
Unlucky forward Sam Philp also suffered an injury blow, undergoing surgery after experiencing a stress fracture to the second metatarsal in a foot.
The 21-year-old played two games midway through 2020 but has not been seen again at senior level.
A timeline on his recovery is uncertain at this stage.
"We are all really disappointed for Sam, given how hard he has worked to get his body right over the last 18 months," Lloyd said.
"He has faced some significant challenges during that time, and while this latest one is frustrating, we'll continue to make sure as a club we are with Sam every step of the way."
Williams and Philp join an injury list that includes gun midfielder Sam Walsh, who has had back surgery and won't feature in the early rounds of the season.
Carlton open the season against Richmond at the MCG on March 16.
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