Ramsey's ACL is intact, according to ESPN, while Ramsey's meniscus requires surgery, according to the NFL Network.
A more catastrophic injury would almost certainly end Ramsey's season.
Ramsey was carried off the field after injuring his knee in a collision with Dolphins WR Tyreek Hill during Thursday's training camp workout.
The initial results of the Dolphins' testing were clearly negative, and surgery was promptly indicated.
Following the departure of Byron Jones, Ramsey was to be teamed with Xavien Howard, and the Dolphins were supposed to have one of the top cornerback tandems in the league.
Instead, Keion Crossen or second-round pick Cam Smith will likely step in for Ramsey until his return.
Ramsey, arguably the best cornerback in the game, has been a three-time All-Pro since being drafted fifth overall by the Jacksonville Jaguars in the 2015 NFL Draft.
Ramsey had four interceptions, 88 total tackles (a career high), two sacks, two forced fumbles, and 18 passes defensed with the Rams last season.