Clady suffered the knee injury playing basketball, two league sources told ESPN NFL Insider Adam Schefter.
Clady has told people he will miss three months, according to the sources.
Team spokesman Patrick Smyth declined to comment on the report when reached by The Associated Press, saying only that veterans were participating this week in the team's offseason training program. Clady's agent, Pat Dye Jr., didn't immediately return a phone call.
Clady was the 12th overall pick out of Boise State in the 2008 NFL draft. He allowed the fewest sacks among tackles as a rookie and last year became the 11th tackle to earn Pro Bowl honors in his second season.
Information from The Associated Press was used in this report.