The trade was first reported by Dan Connolly of the Baltimore Sun.
Parra, 28, is hitting .328 on the year with nine home runs and 39 RBIs. He is eligible for free-agency at the end of the year.
Davies was drafted in the 26th round of the 2011 MLB draft. In 101 1/3 innings in Triple A, he has posted a 2.84 ERA with 7.2 strikeouts per nine innings.
Tom Haudricourt of the Milwaukee Journal-Sentinel reports the Brewers were looking to move Parra in exchange for two players, but settled for Davies. Parra is the second Brewers outfielder traded ahead of the deadline after Carlos Gomez was dealt to the Houston Astros on Thursday.
The Orioles sit in second place in the American League East, six games behind the New York Yankees. The Brewers are in last place of the National League Central Division with a 44-59 record.
- Christopher Chavez