The 34-year-old Brazilian suffered the injury during the Bianconeri's final practice session ahead of yesterday's Serie A opener against Parma, with subsequent tests confirming the worst.
"Lucio has undergone medical tests after twisting his right ankle in training on Friday," read a medical update from the club this morning, issued on www.juventus.it.
"The X-ray and MRI scans, which were conducted on Saturday morning, have revealed a complete tear of the defender's anterior talofibular ligament."
Lucio moved to the Turin club last month after his contract with Inter Milan was cancelled by mutual consent.
Juve began the defence of their Serie A title with a 2-0 home win over Parma yesterday.