The technique as practiced today was pioneered (at least in English) by the New Critics of the mid-twentieth century. It is now a fundamental method of all modern criticism.
Close reading is sometimes called explication de texte, which is the name for the similar tradition of textual interpretation in French literary study.
A truly attentive close reading of a two-hundred-word poem might be thousands of words long without exhausting the possibilities for observation and insight. To take an even more extreme example, Jacques Derrida's essay Ulysses Gramophone, which J. Hillis Miller describes as a "hyperbolic, extravagant...explosion" of the technique of close reading, devotes more than eighty pages to an interpretation of the word "yes" in James Joyce's great modernist novel Ulysses.