Shortly after the St. Louis Rams selected Sam in the seventh round Saturday, Jones tweeted, ''Horrible.'' The tweet was taken down a short time later.
Sam is the first openly gay player to be selected in the NFL draft.
The Dolphins were at the center of bullying scandal last season that embarrassed the league and drew nationwide scrutiny of locker room culture in the NFL.
After the draft, Dolphins general manager Dennis Hickey said he was made aware of Jones' tweet.
''I was disappointed in those comments,'' Hickey said. ''That's not what we stand for as an organization. The draft weekend is the culmination for so many players of their lifetime achievement of their dream to achieve their goal. For Michael Sam, for all the other players, it's such a great celebration as they begin their future.
''We're going to sit down with Don Jones and address (the tweet) appropriately.''
Jones' agent, Chris Martin, said he was unaware of the tweet and declined to comment.
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