The 24-year-old breached the league's policy on performance-enhancing drugs during the off-season and will now miss the first four matches of his side's 2014 campaign.
Jordan told the club's official website: "I recently learned from the NFL that I tested positive for stimulants that are banned under the NFL policy. I worked carefully with my advisors and the union to investigate the test results, and I take full responsibility for the test results.
"I'm very sorry for the impact of this situation on my teammates, coaches, Stephen Ross, the entire Dolphins organisation, fans and my family as well.
"I will continue to work extremely hard during training camp and pre-season. During the suspension, I will stay in top shape and will be ready to contribute upon my return."
Jordan was selected third overall by the Dolphins in the 2013 Draft.