The history of the Karnak Temple complex is largely the history of Thebes. The city does not appear to have been of any significance before the Eleventh Dynasty, and any temple building here would have been relatively small and unimportant, with any shrines being dedicated to the early god of Thebes, Montu. The earliest artifact found in the area of the temple is a small, eight-sided column from the Eleventh Dynasty, which mentions Amun-Re. The tomb of Intef II mentions a 'house of Amun', which implies some structure, whether a shrine or a small temple is unknown. The ancient name for Karnak, Ipet-Isut (usually translated as 'most select of places') only really refers to the central core structures of the Precinct of Amun-Re, and was in use as early as the 11th Dynasty, again implying the presence of some form of temple before the Middle Kingdom expansion.
Read more on Wikipedia