Prado broke the finger in Friday's win against Cincinnati while sliding head-first into home plate on Jason Heyward's 10th-inning double.
After holding him out of the lineup Saturday and Sunday, the Braves made the decision to put Prado on the DL after it was determined he wouldn't be strong enough to grip a bat for at least another week.
Prado is batting .315 with 13 homers and 43 runs batted in this season. He started the All-Star Game as an injury replacement for Philadelphia's Chase Utley.
He will be eligible to return to action Aug. 16.
The Braves recalled infielder Diory Hernandez from Class AAA Gwinnett to take Prado's spot on the roster.