Hargreaves was injured while attempting to break up a pass intended for New Orleans running back Alvin Kamara in the fourth quarter of Sunday's 48-40 victory over the Saints.
The 23-year-old Hargreaves recorded seven tackles, a pass breakup and a forced fumble prior to departing for the Buccaneers (1-0), who will host the Philadelphia Eagles (1-0) on Sunday.
Hargraves, who is listed at 5-foot-10 and 204 pounds, will have to sit out at least eight games for a Buccaneers' secondary that was ravaged in the season opener while playing without fellow cornerback Brent Grimes.
Grimes sustained a groin injury during Friday's practice. The four-time Pro Bowl selection had 49 tackles and three interceptions last season.
Hargreaves has collected 125 tackles, two forced fumbles and one interception in 26 career games since being selected by the Buccaneers with the 11th overall pick of the 2016 NFL Draft.
Also on Wednesday, the Buccaneers re-signed defensive end Will Clarke. The 6-6, 275-pound Pittsburgh native posted 29 tackles, 2.5 sacks, two passes defensed and one fumble recovery in 15 games last season.
Tampa Bay also signed offensive tackle Jarron Jones to the team's practice squad. Jones, who is listed at 6-6 and 320 pounds, has spent time on the practice squads of the Dallas Cowboys and Seattle Seahawks during the regular season.