A person is not permitted to strike a parent – even if they’re striking him – unless he’s truly in danger and it constitutes self-defense.
The Sefer HaChinuch asks a logical question: the Talmud teaches us that the Torah does not mandate a punishment unless the prohibition is stated elsewhere. (See, for example, Sanhedrin 54a.) This verse states the punishment, but where is the prohibition? (The Rambam actually addresses this question several times so by the time he comes to this mitzvah, it’s “old news.” In our chronological listing of mitzvos, however, it’s the first time we come to this issue.)
Really, a person is not allowed to strike anybody, as we’ll see IY”H in Mitzvah #595. One’s parents are included in that general prohibition. However, the Rambam tells us in Sefer HaMitzvos (Negative Mitzvah #26) that one prohibition in the Torah can actually apply to several different mitzvos if they have discrete punishments. (He refers us to his ninth and fourteenth principles for identifying the mitzvos for more clarity.) Since striking a parent has a very different penalty from striking just anyone, not doing so is counted as an independent mitzvah.
We have already discussed the importance of honoring one’s parents. This prohibition is the flip side: raising a hand to a parent is the ultimate in disrespect. While it is always prohibited to strike a parent, one only becomes liable if he draws blood. This prohibition is so severe that, under normal circumstances, a doctor or nurse should not treat their own parent, since injections, IVs, tests, etc. can lead to bleeding and bruising. (Of course, since the intention is to heal rather than to harm, one may do so if another professional is unavailable – see Talmud Sanhedrin 84b.)
This mitzvah applies to both men and women in all times and places. It is discussed in the Talmud in Sanhedrin 84-85 and in the Shulchan Aruch in Yoreh Deah 241. It is #319 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #44 of the 194 negative mitzvos that can be fulfilled today in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.