Miller has made one appearance at the FIFA World Cup so far, playing the full 90 minutes of a 0-0 draw with England in their final Group D fixture.
Costa Rica made history on Sunday, with a penalty shootout victory over Greece seeing them progress to the quarter-finals for the first time.
They will take on the Netherlands in Salvador on Saturday without Oscar Duarte, sent off for two yellow cards against Greece, with Miller previously a potential candidate to replace him.
However a statement released by the Costa Rican Football Federation confirmed that the New York Red Bulls man would not be available for selection.
"A hamstring strain in the left leg of Roy Miller precludes the defender from selection for the quarter-final phase," it read.
"The doctor, Vladimir Badilla, reported that after an MRI scan it was determined that the player has a grade one injury which will keep him sidelined for several days.
"The injury occurred last Friday when, at the end of training practising penalty kicks, Miller felt the pull with his last shot."
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