The 23-year-old right-hander, who missed out on a rotation spot at season's start after command issues plagued him all spring, has worked his way through those at Triple-A Sacramento. Parker is 1-0 with a 2.18 ERA with 21 strikeouts and six walks in 20 2/3 innings across four starts.
"He's been pitching well," Melvin said. "We've always envisioned him being here at some point in time, especially with the stuff he has."
Parker's looming promotion comes in the wake of Graham Godfrey's return to Triple-A. Parker was the key piece of December's trade that sent All-Star Trevor Cahill to Arizona, where Parker was considered the D-backs' No. 1 prospect.
Following rehab from his 2010 Tommy John surgery, Parker posted an 11-8 record and 3.79 ERA for Arizona's Double-A club last year. He was called up to the big leagues for the first time in September and impressed greatly in just one start, tossing 5 2/3 scoreless innings and earning a spot on the club's postseason roster.
Parker will be pitching on three days' rest, but he utilized just 48 pitches in his Saturday start.