Parra, one of the team's top prospects, suffered the injury while batting in Thursday night's game against the Chicago Cubs.
"It's extremely disappointing," he said.
The left-hander said he hoped to pitch in two weeks, but acknowledged he was unsure when -- or if -- he would return this season.
"They put me on the 15-day DL, so maybe right around that amount of time," Parra said.
Manager Ned Yost said he was unsure of the timetable.
"I don't know," Yost said. "His finger is broken and he's not pitching. I've got more pressing concerns. When his finger starts to get a little bit better and if he can throw, we'll see how much time he has left."
Right-hander Claudio Vargas was placed on the 15-day DL on Tuesday with a lower back strain.
The team recalled right-hander Greg Aquino from Triple-A Nashville to take Parra's spot in the rotation.
Vargas' back improving: Vargas reported that his strained lower back was improving.
"It's all good," he said.
When asked whether he should be able to pitch when eligible to come off the DL in mid-September, he said, "Oh yeah, I think so. If it keeps going like this, I see it now. I'll begin throwing next week."
Yost feels for Capuano: The team has lost each of the last 18 games in which Chris Capuano has pitched, but Yost said the left-hander was not pitching poorly.
"Poor Cappy," he said. "Capuano just cannot catch a break."
Capuano replaced Parra on Thursday night with the score tied at 3, but gave up two consecutive home runs in Chicago's 5-3 victory to lose a team-record 12th straight decision.
"He has absolutely no leeway for mistake," Yost said. "When he does give up a home run, it breaks his back and it makes it look worse than it really is.
"Every time he makes one bad pitch, it's very glaring. He's pitching so much better than anybody's giving him credit for, and it's just not happening for him now."
Villanueva, Spurling to rejoin team: Yost said right-handers Carlos Villanueva and Chris Spurling would be among "four or five" players called up from the Minors on Saturday, when rosters expand to 40 players.
Villanueva is the leading candidate to start Tuesday night, when the Brewers host the Astros.
Yost would not divulge all of the players slated for recall, but said a third catcher would be added. That could be Racine, Wis., native Vinny Rottino, who is on the team's 40-man roster. Nashville's starting catcher, Mike Rivera, is not on the 40-man roster and would have to be added to be called up to Milwaukee.
Walk of Fame ceremony: Former Milwaukee Braves players Warren Spahn and Eddie Mathews, and former Braves general manager John Quinn were inducted into the Miller Park Walk of Fame on Friday night.
The families of Mathews, Quinn and Spahn participated in a ceremony before the Brewers game against the Pittsburgh Pirates as the team unveiled the newest plaques on the Walk of Fame.
"Eddie's heart and soul really was the Milwaukee Braves," Mathews' widow, Judy, said at the ceremony.
Past winners of the award are Hank Aaron, Rollie Fingers, Paul Molitor and Robin Yount in 2001; Commissioner Bud Selig and Cecil Cooper in 2002; Bob Uecker and Harry Dalton in 2003; Jim Gantner and Gorman Thomas in 2004; and Don Money and Harvey Kuenn in 2005.
The Braves played in Milwaukee from 1953-65, winning the World Series 50 years ago in 1957.
Brewer bits: When Rickie Weeks homered to lead off Thursday night's game against the Chicago Cubs, it was the first time this year he has homered to lead off a game. Weeks entered Friday night's game with a 10-game hitting streak. ... A day after moving up to second in the batting order, J.J. Hardy was back in the eighth spot Friday night.
On deck: Right-hander Dave Bush (10-9, 4.96 ERA) will attempt to get his first career victory against Pittsburgh when he takes the mound for the Brewers on Saturday night at 6:05 CT. He is 0-3 with a 5.85 ERA in four appearances, three starts, against the Pirates. Left-hander Shane Youman (3-4, 5.59), who earned his first Major League win July 3 against the Brewers, will make his first start since Aug. 13 for Pittsburgh.
Joe DiGiovanni is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.