Q. If someone davens every Shabbath in a minyan that finishes late (after chatzos), and therefore, due to his medicinal needs, he privately makes a fast kiddush after shacharis and eats just a kezais mezonos. Can he do so on Parshas Zachor, since in this day it is a mitzva of the Torah and one shouldn't eat before?
A. Shulchan Aruch (O.H. 652: 2) rules in regards to the mitzva of lulav on the first day, that one should not eat before complying with a mitzva of the Torah. Nitei Gavriel (Purim 19: 9) asserts that the same applies on Shabbos Parshas Zachor, and one should not eat more than an "achilas arai" or a transient small amount.
Similarly, Mishna Berura (ibid. 7) maintains that in need, one may take a taste. He adds, that if he will be reminded of the mitzva to be done, he may also be lenient.
Piskei Teshuvos (ibid. 4) defines "achilas arai" as less than a beitza (an egg-full, about 56g), equal to two kezaisim.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a