An Etymological Dictionary of the German Language/Mühle
Mühle, f., from the equiv. MidHG. mül (müle), OHG. mulî, mulîn, f., ‘mill’; comp. AS. myln, E. mill, OIc. mylna (derived from E.), f., ‘mill.’ Hardly a Teut. derivative of the root mal, discussed under mahlen; it is rather borrowed from common Rom. môlina, ‘mill’ (for classical Lat. mola); comp. Ital. mulino, Fr. moulin, ‘mill’ (Du. molen, OIr. mulen, and Slav. mŭlinŭ. The formation of an OTeut. *mulînô with a suffix -înô has no parallels in Teut. The genuine Teut. word for ‘mill’ is preserved in Goth. qaírnus, AS. cweorn, OHG. quirn.