After beating Twins left-hander Francisco Liriano on Thursday in Minneapolis, Colorado will see two lefties against Milwaukee (Parra and Randy Wolf) and two against Boston next week (Jon Lester and Felix Doubront).
"We're going to get our fair share of them," Rockies manager Jim Tracy said.
The Rockies are 11-9 against left-handed starters this year, including wins in the past three games in which they've faced a lefty starter.
Colorado also has seven position players who are batting .250 or better against lefties this year.
Meanwhile, Parra (1-4, 4.04) has an ERA of 7.59 against left-handed hitters, who are batting .408 against him this year.
"We did play on the fact that he's having trouble getting some left-handed hitters out, so we're going to give him so left-handed hitters to try to get out," Tracy said.