According to ESPN's Dan Graziano, there is no timetable for Ramsey's return, but he is not expected to miss any regular-season games.
The injury occurred during OTAs, and Ramsey released the following statement through the team:
"To all my supporters and fans, I want you to know that I chose to undergo surgery to treat a minor injury that was very successful. I want to and will be the best version of myself that I can be for the upcoming 2017 season.
"I will attack this rehab, refine my body and work as hard as I ever have to become the best Defensive Back in this league and to make everyone, including my family, teammates and city, proud of who I am.
"I can’t wait to be back on the field with the team and show the world how we're rocking this year."
The Jags selected Ramsey with the No. 5 overall pick in the 2016 NFL draft out of Florida State, and he made an instant impact.
Ramsey started all 16 games, registering 65 tackles, 14 passes defended and two interceptions, one of which was returned for a touchdown.
The 22-year-old is penciled in to start across from marquee free-agent signing A.J. Bouye in 2017.
Jacksonville is somewhat lacking in terms of quality depth behind Ramsey and Bouye, but the likes of rookie seventh-round pick Jalen Myrick, as well as Josh Johnson, Doran Grant and others will likely see an uptick in snaps during Ramsey's absence.