Miami also optioned outfielder Jake Marisnick to Triple-A. Shortstop Adeiny Hechavarria (right triceps strain) will be reinstated on Sunday and play in the series finale against the Cardinals at Busch Stadium.
Right-hander Tom Koehler also is returning from the paternity list, after his wife, Ashley, gave birth to a girl. Koehler will start in the series opener at Arizona on Monday.
"I'm not going to feel sorry for myself," Heaney said. "I'm going to go try to get better. I want to be back up here. Everybody has the same goal. I'm not going to say I can't do it. I have stuff I need to work on. This wasn't the best me I can be."
After seeing signs of struggle in his first three big league starts, the Marlins weighed how to handle Heaney entering Saturday, when he gave up five runs on eight hits in 3 2/3 innings.
"He's going to be a great pitcher in this league for a long time," manager Mike Redmond said. "He's got great stuff. He just faced probably two of the best teams in baseball. It was a great learning experience. He knows he can pitch up there. Are there areas he needs to work? Of course. You can say that about a lot of guys."
Heaney, ranked as the 25th overall prospect by MLB.com, certainly has had a tough draw of late. Before facing the Cardinals, he took on the A's at Marlins Park, giving up four runs in six innings.
Heaney is 0-3 with a 6.53 ERA in 20 2/3 innings.
"I've got stuff I need to work on, obviously," said Heaney, the ninth overall pick in the 2012 First-Year Player Draft. "This is not how I want to pitch."
In Minor League stints this year with Double-A Jacksonville and New Orleans, Heaney was 7-2 with a 2.47 ERA, giving up three home runs in 76 2/3 innings.
The long ball has plagued Heaney, who has allowed five in his four big league starts.
"Good hitters hit bad pitches," Heaney said. "You keep making bad pitches, I don't care what level you're at, you're going to give up hits. And up here, they happen to be homers. Triple-A, they might be doubles. [Class A], they might be singles, but they're going to hit the ball regardless."
With an off-day on Thursday and then the All-Star break, the Marlins plan on going with four starting pitchers for now.
Henderson Alvarez will start on Sunday against the Cardinals. For the series at Arizona, the Marlins will go with Koehler (Monday), Brad Hand (Tuesday) and Nathan Eovaldi (Wednesday).
After Thursday's off-day, the final series before the break will begin at Citi Field against the Mets on Friday. Miami is planning on going with Alvarez (Friday), Koehler (Saturday) and Hand (Sunday).
Heaney will head to New Orleans to work on polishing up his overall game, from pitching, fielding position and doing a better job with the bat, like bunting.
"We talked about it when we brought him up, we were going to protect him," Redmond said. "His next start was Thursday, the off-day, and we talked about skipping him and getting him some extra rest anyway.
"This guy was in [Class A] Jupiter last year. We want to make sure he's confident and right. These guys up here are really good hitters. Your game has got to be tight, and you got to be able to pound the strike zone and understand lots of different things. We talked about making sure we took care of him, and this gives us a chance."