Parra was drafted by the Milwaukee Brewers in the 26th round of the 2001 Major League Baseball draft. Shoulder problems resulted in a slower-than-expected advancement through the Brewers' minor league system for the draft-and-follow prospect. They had also hindered the left-hander's ability to pitch deep into games, having only gone over 100 innings pitched in his 2003 season at Class A Beloit. After beginning the 2006 season at Class A-Advanced Brevard County, he was promoted to Double-A Huntsville in August and selected to participate in that year's Arizona Fall League. Through 5 years of professional baseball, Parra had a career minor league record of 28–15 with a 3.22 ERA. He had pitched just two complete games during this period. At the time, Parra relied primarily on his four-seam fastball but also utilized a curveball and split-finger fastball.