Boston manager Terry Francona said Friday that Beckett felt well enough to pitch this weekend but that "it wasn't in his best interest." Francona said the delay will allow Beckett to go through his normal preparation before facing the NL East-leading Phillies.
Beckett is 6-2 with a 1.86 ERA, tops in the American League.
Miller made his Red Sox debut on Monday, yielding three runs in 5 2/3 innings against San Diego.
Information from The Associated Press was used in this report.