Moore (8-0) started Friday night against Cleveland but didn't return after pitching the first inning because of the game's third rain delay, which lasted 2 hours and 39 minutes.
Rays manager Joe Maddon said Moore could have started Sunday but the Rays chose to stick with Jeremy Hellickson. Tampa Bay is off Monday and begins a three-game series in Detroit. Moore was originally scheduled to pitch the series finale Thursday but Maddon decided to move him up two days.
Right-hander Alex Cobb, who missed his last start because of a cut finger, will start Wednesday while Roberto Hernandez will pitch Thursday.