The news came on the same day that NFL.com reported that Indianapolis Colts wide receiver LaVon Brazill has been suspended for at least one season without pay for violating the league's policy on substance abuse.
Jordan, the number three overall selection in the 2013 NFL draft, can take part in all off-season and pre-season training and games.
"We were disappointed to learn about Dion's suspension," Dolphins head coach Joe Philbin said. "Dion has accepted responsibility for his actions and is committed to improving, both on and off the field, in preparation for the upcoming year."
Jordan also released a statement through the team.
"I recently learned from the NFL that I tested positive for stimulants that are banned under the NFL policy," he said.
"I worked carefully with my advisors and the union to investigate the test results, and I take full responsibility for the test results."
Jordan played in all 16 games for Miami in his rookie campaign, compiling 26 tackles and two sacks.
Brazill's ban wold be the second of his brief career, after a four-game suspension last year for violation of the league's drug policy.
At the time, he said it was time to choose between "money or marijuana."