Williams suffered the injury a week before mandatory minicamp, which began June 11.
"We look forward to Jonah being a major contributor in the future, and know that he won't let this injury deter him from still being an important part of this team," head coach Zac Taylor said in a statement.
"We're confident in our offensive line personnel as we head into training camp, and we believe they can do their part in helping this team achieve its goals."
Williams was the first offensive lineman taken in this April's draft. Coming out of Alabama, he was viewed as the best left-tackle prospect. Veteran Cordy Glenn, whom Cincinnati acquired via trade last March, was expected to move to left guard to accommodate Williams. He'll likely remain at his natural position while the rookie is sidelined.
Of the Bengals' last four first-round picks, including Williams, 2016 pick William Jackson missed his entire rookie season with an injury, and 2017 pick John Ross played in just three games his first year. Last year's first-rounder, Billy Price, played in and started 10 games.