The moves were announced following a 3-0 loss to San Francisco on Saturday night.
Morrison had been struggling offensively and defensively in recent weeks, hitting .230 in his last 38 games. Overall, Morrison is hitting .249 with 17 home runs and 60 RBI.
Following the resignation of manager Edwin Rodriguez in June, Morrison was reprimanded by the team for comments he posted on his Twitter account.
Morrison said he feels "resentment" and "anger" over the decision.
Helms was batting .191 overall. He had seven hits in 33 at-bats as a pinch hitter.
The Marlins said they will announce moves Sunday to fill the open roster spots.