The injury was revealed in an MRI exam Monday.
The Braves announced the move following their 5-0 win over the Washington Nationals. Heyward was held out of the Braves' starting lineup for the third straight game.
"We're doing the best thing, I believe," Heyward said after the game. "Right now is a good opportunity to get it done, get the rest done, get the strength back so I'll be able to come back the second half."
Heyward tried to play through the injury for about six weeks. He was given a cortisone shot on Monday night and the thumb will be placed in a cast.
The 15 days on the disabled list could jeopardize Heyward's possible spot on the NL All-Star team. He ranks second among outfielders in the early NL voting.
Heyward, the NL's rookie of the month for April and May, will be eligible to come off the DL during the July 12-14 All-Star break. The Braves expect Heyward back in uniform when the team opens the second half of the season on July 15.
"I don't know what the All-Star situation is," Heyward said. "Whatever MLB says they would like to have. If I can go and give thanks to the fans and show up for them when they voted me in, I would like to. If MLB says we respect what the Braves want for Jason, playing rehab games before he comes back, then I'm open to that, also."
Heyward's batting average has dropped to .251, the low mark for the rookie outfielder since April 30. He is in a 1-for-16 slump.
Heyward leads NL rookies with 11 homers and 45 RBI.