The Mishna, Avodah Zarah, 35b, states that it is prohibited to eat food that was cooked by a non-Jew (bishul akum). This prohibition applies even if all of the ingredients are assumed to be kosher.
Bishul Akum includes foods that are cooked, baked, roasted, fried or broiled by a non-Jew. The Rama (Y.D. 113:3) writes that only food cooked using “fire” is prohibited by bishul akum.
In recent years, questions have been raised on the halachic status of microwave cooking. With conventional cooking, a source of existing heat is transmitted, which penetrates into the food and surrounding area by a process called convection. With microwave cooking, energy waves (i.e. microwaves) are generated that cause a molecular movement in the food substance. This movement causes friction between the molecules and in effect causes the food to heat itself. Because no form of “fire” is present in the cooking, there is reason to inquire whether microwave cooking is permitted.
With regard to hilchos Shabbos, the poskim debate whether cooking with a microwave is a biblical form of cooking or is it merely rabbinic. According to Harav Shlomo Zalman Auerbach zt”l (SS”K 1:127) microwave cooking is not biblically prohibited, while Harav Moshe Feinstein zt”l (Igros Moshe 3:52) rules that since microwave cooking is a common form of cooking, it is biblically forbidden. Harav Noach Isaac Oelbaum shlit”a (Minchas Chein vol. 1 page 177) discusses the use of microwaves with regard to bishul akum and he explains that according to Harav Moshe zt”l food cooked by a non-Jew in a microwave oven is considered bishul akum.16 A strict view was also expressed by Harav Shmuel Wosner zt”l (Shevet Halevi 8:185), Harav Shraga Feivish Schneebalg zt”l (Shraga Hameir 6:52:3) and Harav Yosef Shalom Elyashiv zt”l (Shvus Yitzchak vol. 6 page 61).
However, there were poskim who permit food cooked by a non-Jew using a microwave. The arguments for leniency are that when one cooks with a microwave he is not cooking by fire and that microwave technology was not available at the time when Chazal promulgated the Bishul Akum decree and thus was not included in the prohibition. Moreover, most food cooked in a microwave does not taste as good as food that is prepared on the stove. A permissible view can be found in the Seforim Chelkas Binyamin (page 106), Lehoros Nasan (7:64) and Rivevos Efraim (8:111). Similarly, Harav Moshe Heinemann shlit”a, in an article on the Star-K website, writes, “Bishul akum does not apply to microwaved food. The rabbinical prohibition of bishul akum applies only to conventional cooking methods through fire (e.g., cooking, frying, roasting). Food prepared through microwaving is not included in the prohibition.”
Harav Asher Weiss shlit”a (Minchas Asher Devarim) discusses this question and he concludes that one may rule leniently in case of great need. Likewise, Harav Oelbaum shlit”a discusses this issue at length and he concludes, “The poskim debate whether food cooked in a microwave is subject to the laws of bishul akum. While one should initially (l’chatchila) rule stringently, b’dieved one may be lenient.”
If the food was fully cooked by a Jew, a non-Jew may re-heat it in the microwave. Once a food is cooked there is no concern of a non-Jew re-heating it.