Jones, who will have season-ending surgery, faces a four to six month recovery, a source told ESPN's Adam Caplan.
While Jones' season is over, cornerback Chris Culliver is slated to practice for first time this year, sources told ESPN's Adam Schefter.
Jones suffered his injury in Sunday's victory over the Pittsburgh Steelers. Jones had sought a second opinion in the hopes he could return at some point this season.
The loss of Jones is a major blow for Miami's 27th-rated defense. Jones is second on the team with 51 tackles, and he picked up his first interception of the season off Pittsburgh quarterback Ben Roethlisberger on Sunday.
Last season Jones led Miami in tackles (135) and interceptions (five) on his way to his first Pro Bowl.
Backup safety Michael Thomas will replace Jones in the starting lineup.
Culliver was placed on the physically unable to perform list when he signed with the Dolphins in August as he was recovering from a knee injury he suffered last November. He was released by the Redskins in May after completing just one season of a four-year contract he signed with the team in 2015.
His 2015 season ended on Thanksgiving Day, when he suffered a torn ACL and MCL in his right knee during a practice. He started six games before his injury.
ESPN's James Walker contributed to this report.