The 33-year-old perennial All-Star had played in all 56 games this season, averaging 38.4 minutes, fourth-most in the NBA. The Lakers are a half-game ahead of the Los Angeles Clippers in the Pacific Division. He played in all 82 games last season.
The game against the Suns was the first of a three-game road trip, with later stops at New Orleans on Monday and a critical showdown with San Antonio on Wednesday.
Bryant averaged 38.5 points in three games against Phoenix this season, two of them Los Angeles wins.
Vitti described the area that is injured as a sheath, such as the one that would hold a knife, with the tendon surrounded by it.
Bryant has had to adjust this season to the arrival of a new coach in Mike Brown following the retirement of Phil Jackson, who coached the Lakers to five NBA titles. Earlier this season, Bryant became the youngest player in NBA history to reach 29,000 points. He is fifth on the NBA's career scoring list, behind Kareem Abdul-Jabbar, Karl Malone, Michael Jordan and Wilt Chamberlain.