"I promise I will attack this rehab and be back stronger than ever," Ramsey posted to X, formerly Twitter. "This will just [be] part of the greater story down the stretch! Adversity is opportunity!"
Ramsey was injured toward the end of Thursday's practice and was carted back to the locker room after practice concluded. An MRI on Thursday evening revealed damage to his meniscus.
Earlier Friday, coach Mike McDaniel said the timeline for Ramsey's return is undetermined, but the beginning of the regular season is not a realistic target.
"The length of this rehabilitation is kind of dictated on a couple things that could occur in the surgery," McDaniel said. "So the exact timeline is a little too big to be determined. What I can tell you is I don't think the beginning of the regular season is really part of the scenario. It's going to be into the season, and how deep that is depends on what happens today."
A source told ESPN's Adam Schefter on Thursday that Ramsey could miss "a few months," depending on how the surgery goes.
Ramsey spoke to his teammates Thursday, assuring them he will return from the injury and demanding that they need not worry or feel sorry for him.
Second-year cornerback Kader Kohou and 2023 second-round pick Cam Smith are next in line to fill the void in Miami's secondary. Kohou, in particular, drew praise from four-time Pro Bowler Xavien Howard as a player to watch even before Ramsey's injury.
"I see determination and hunger to build on what he's really done," McDaniel said. "That's kind of why Kader's a prime example of seeking opportunity, and every player is very aware of that. Last year we were sitting here talking about Byron Jones and my answer to you guys was not, 'Oh yeah, Kader.' ...
"The development, the consistency and the growth that determines who's playing and who's excelling -- just like Kader showed -- that's why you breed competition. You get as many quality players as you can, and then you let the chips fall as they decide."
The Dolphins have the fourth-toughest schedule in the NFL, according to ESPN's Football Power Index, and begin the season on the road against the Los Angeles Chargers on Sept. 10.