"pertaining to the geological period between the Oligocene and Pliocene," 1831, irregular formation from Greek meion "less" (from PIE root *mei- (2) "small") + -cene "new, recent." The intention is "the middle division of the Tertiary period."
A typical example of the monstrosities with which scientific men in want of a label for something, and indifferent to all beyond their own province, defile the language. The elements of the word are Greek, but not the way they are put together, nor the meaning demanded of the compound. [Fowler]