Masterson (4-5, 4.75 ERA) owns baseball's fifth-worst road ERA at 6.20, while Miley's 5.40 home ERA is sixth-worst in the majors.
Masterson's lone start against Arizona came in 2008, so the right-hander will get his first look at Diamondbacks star Paul Goldschmidt.
Goldschmidt leads the club in batting average (.308), home runs (15) and RBIs (52). Indians pitching coach Mickey Callaway is looking forward to seeing the slugger face Masterson, who has a 3.32 ERA in his last four starts.
"Obviously he's really good," Callaway told MLB's official website. "I think Masty will match up good, sink him down and in. The movement Masty gets, it's one of the best sliders in baseball, so I think that will be a good matchup."
The Indians are 9-15 against left-handed starters as they face Miley (3-6, 4.62) for the first time. Miley is 0-3 with a 4.37 ERA in his last seven starts.
These teams are back in action after much-needed off days.
Cleveland (37-39) capped a 2-4 homestand by getting swept over the weekend by Detroit to fall five games behind the first-place Tigers in the AL Central. The Indians now start an eight-game trip that includes five interleague games.
"Is it disappointing? Of course, we just got swept at home," said second baseman Jason Kipnis, who went 1 for 14 in the three-game series. "But at the same time, we swept them last time they were here and now look where they are, they're back in first place. So it just goes to show you how long the season is. It goes to show you how tight this division is."