A staple in Miami's secondary the past five seasons, Jones will not be eligible to play in a regular-season game until Oct. 12 against the Green Bay Packers. He was second on the team with 107 tackles last season and had one interception.
Defensive end Dion Jordan received a four-game suspension on July 3 for a similar violation.
"I was very disappointed when we found out about Reshad's suspension," coach Joe Philbin said in a statement. "When we talked to him, Reshad pledged to learn from this situation.
"Our secondary as a unit, including Reshad, has performed well this offseason and I have complete confidence in the group as we progress through training camp and into the regular season."
In addition to Jones and Jordan, Miami also is expected to be without Pro Bowl center Mike Pouncey (hip) for the start of the regular season.
Jones apologized via a statement released by the Dolphins and NFLPA on Friday.
"I recently learned from the NFL that I tested positive for substance that is banned under the NFL performance-enhancing substances policy," Jones said in the statement. "I worked closely with the union to investigate what happened, and I learned that a supplement I took caused the positive test. I deeply regret not investigating the supplement carefully before I took it, and I will never again take a supplement without having it checked.
"I am very sorry for the effect of my mistake on my teammates and coaches. I apologize to them, the Dolphins organization, and fans. During the time away from the team, I will participate in an intense training program so that I can help my team as soon as I return."