Q. A teacher or a Rabbi who has severe dandruff problems and the dandruff constantly falls on his clothes, sometimes making it significantly dirty, is it a violation (the talmid chacham's clothing has to be clean at all times)? May one brush it off on Shabbos? Does one need to stop learning or davening to brush it off?
A. Poskim disagree whether the removing of dust or other dirt particles from a garment is considered laundering, a prohibited melacha on Shabbos. Sefer HaZichronos, (quoted by Magen Avrohom 302: 4) and others maintain that removing any fleck of dirt from a garment, even if it is not absorbed into the fabric of the garment, and only lying on its surface, like a loose thread or feather, is a Biblical prohibition. Tosafos, (Shabbos 147a) and many others assert that removing any dirt, whether it is absorbed into the fabric, like dust or not, is totally permitted, since a dusty garment is not considered dirty and removing the dust is not considered laundering. Rashi, (Shabbos 147a,) Remah and Biur Hagra 302:1, and others opine that only dust which is trapped between the fibers of the garment should not be removed, while dust which lies on the surface is permitted.
Most Poskim allow the removal a feather or a loose thread or light dust that has landed on the garment, when using one’s hands or a soft, dry cloth, but not a brush, and the garment it is not shaken or scrubbed vigorously. (See Mishna Berura 302: 36 and Biur Halocho 302:1. see also question 2282, regarding laundering during the Nine Days).
Horav Shlomo Miller's Shlit'a opinion is that it also applies to dandruff. The Rov added that although it should be removed continually as it appears, it should not be removed during the amida.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a