The Shulhan Aruch (Orah Haim 303) explicitly forbids combing one’s hair on Shabbat, given that combing invariably results in the removal of some hairs from the head (listen to audio recording for precise citation). Pulling hair from one’s head on Shabbat falls under the category of Gozez – shearing. During the construction of the Mishkan, the hair of animals was removed from the skin as part of the process of preparing the skin for use in the Mishkan. Since the Shabbat prohibitions are modeled after the categories of work done in the construction of the Mishkan, it is similarly forbidden to remove hair from one’s head on Shabbat. As a result, one may not comb his hair, as this always causes hairs to be removed.
At first glance, one might argue that this should be permissible on Shabbat due to the principle of "Melacha She’ena Sericha Le’gufa." This principle makes an exception in cases where the person’s action is not intended for the purpose of the Melacha (forbidden act). Here, the individual’s intent is to comb his hair, not to remove hair, and this would therefore seemingly qualify as a "Melacha She’ena Sericha Le’gufa." The Ran (Rabbenu Nisim of Gerona, Spain, 1290-1380), however, refutes this argument, noting that in the original Melacha of Gozez, during the construction of the Mishkan, the intent was not the removal of the animal’s hair per se. The hair was removed for the purpose of preparing the skin, and not to use the hair. Therefore, since the model of Gozez is a case where the act was not performed for the purpose of hair removal, the prohibition similarly applies to all cases of hair removal, even if this is not the person’s objective or intent.
Another argument that could be raised is the fact that one has no interest in removing hair while combing. His concern is not that hairs should fall, but rather that he look presentable, and therefore perhaps it should be permitted. The Sha’ar Ha’siyun (notes to the Mishna Berura by that work’s author, Rabbi Yisrael Meir Kagan, 1839-1933), however, notes that since one cannot comb his hair without causing hairs to fall, he is considered as though he wants the hairs to fall, and combing is therefore forbidden.
The Mishna Berura cites the Yeshu’ot Yaakob as decrying the fact that so many people are unaware of or unwilling to accept the prohibition against combing hair on Shabbat (listen to audio recording for precise citation). The Yeshu’ot Yaakob condemns these people as willful Shabbat violators who actively desecrate the Shabbat by combing their hair. The Mishna Berura exhorts Rabbis to teach their congregations about this prohibition, so that hopefully at least some people will be alerted to this issue and will refrain from combing their hair on Shabbat.
One should therefore arrange his hair on Shabbat with either his hands, or with a soft-bristle brush that does not uproot hairs. Women must also be instructed to comb their hair with only soft-bristle brushes, and not with regular combs.
Interestingly, the Maharam Shick (1807-1879) wrote that if a person appears in the synagogue on Shabbat with combed hair, he is classified as a public Shabbat violator, as he must have violated the prohibition of combing hair on Shabbat. We, however, do not follow this view, given the possibility of combing in permissible fashion, as discussed. A person who appears with combed hair may be given the benefit of the doubt that he combed his hair through permissible means. In any event, this is a Halacha of which many people are unfortunately unaware, and something that we should all be mindful of.
Summary: It is strictly forbidden to comb one’s hair on Shabbat, except with one’s hands or with a soft-bristle brush. This applies to both men and women.