The 31-year-old went off injured after half an hour in Sunday's 2-1 win over Lazio in Rome.
"Bonucci suffered a sprained right ankle ... around the joint capsule," Juventus said in a statement.
According to reports the defender could be out of action for up to a month.
The Italy international has already begun treatment but could miss the Champions League tie in Madrid on February 20. The second leg will be in Turin on March 12.
Bonucci returned to Juventus this season after an unsuccessful year at AC Milan and has reestablished himself as one of Massimiliano Allegri's key players.