One of the thirty-nine Melachot (categories of activity) forbidden on Shabbat is "Dash," or "threshing." The processing of grain requires removing the kernel from the inedible shell that surrounds it, and this was done either with animals that would stomp on the grain, or with sticks that were used to break the shells.
Halacha extends this Melacha to include any act of "Mefarek" – removing food from an inedible substance that surrounds it. The question thus arises as to whether a mother may nurse an infant on Shabbat, or express breast milk on Shabbat. Removing milk from the breast is precisely a case of Mefarek, where an edible substance is removed from a surrounding, inedible substance.
However, the prohibition of Mefarek is subject to an important restriction, namely, that it does not apply when the food is removed "Derech Achila," through the standard process of eating. For example, Halacha clearly allows one to eat pistachio nuts on Shabbat, despite the fact that this entails cracking the outer shell to remove the nut. Since this is done as part of the normal process of eating, the prohibition of Mefarek does not obtain. This provision would clearly apply to nursing, as well. Since the normal manner for an infant to eat is by extracting the mother's milk from the breast, nursing does not constitute a violation of Mefarek. Moreover, this provision of "Derech Achila" allows a mother to squeeze some milk to help the infant latch onto the breast, as many infants require. Since this squeezing is done as part of the eating process, it does not violate the prohibition of Mefarek.
However, although it is permitted for a woman to squeeze a bit of milk for her baby as part of the nursing process, Halacha would forbid expressing milk into a bottle or container. Since this is not done as part of the eating process, it indeed constitutes a violation of Mefarek and is forbidden. (Menuhat Ahava, Helek2, page 180-183)
What, then, should a woman do if she feels engorged and the baby refuses to nurse?
The Halachic authorities (including Chacham Ovadia Yosef and Shemirat Shabbat Ke'hilchata, perek36:20) rule that in such a case, a woman can express milk in a manner whereby it immediately becomes inedible. For example, she can pump the milk directly onto the floor or into a drain. Alternatively, she can place some soap or other inedible substance into the bottle or container into which the milk is expressed, so that it immediately becomes unfit for consumption. In this way, she is not considered extracting food, and she thereby avoids the prohibition of Mefarek. Chacham Ovadia Yosef, in Kol Sinai page 272, cites a view allowing the woman to express her milk into a normal bottle or container and then immediately discard it. He writes that when it becomes necessary one may rely on this view, but preferably the woman should place some substance in the bottle so that the milk becomes spoiled immediately after being extracted. (Menuhat Ahava, Helek 2, pages 184-185)
Is expressing milk permissible if the infant requires breast milk but cannot nurse properly?
In such a case, where an infant requires specifically the mother's milk and does not nurse from the mother, Halacha considers this a situation of potential risk to the infant's health, and thus allows the mother to express milk normally into a bottle. This dispensation applies only if the infant cannot drink formula, and thus no alternative to breast milk is available; otherwise, the infant must be given formula.
The work Menuhat Ahava (ibid) writes that in such a case, where Halacha permits the mother to express milk into a bottle for the infant to drink, she should preferably express only a small amount at a time (teaspoon and a half.) Even though she is permitted to express milk due to the extenuating circumstances, it is preferable to rely on this leniency as minimally as possible, and therefore she should try to express in small amounts.
Summary: A woman is permitted to nurse an infant on Shabbat, and to squeeze some drops of milk if this is necessary to help the infant latch onto the breast. She may not, however, express milk into a bottle or container. If she feels engorged and the baby is not nursing, she may express the milk in a manner whereby it immediately becomes spoiled, such as on the floor or over a drain, or by placing a substance such as soap into the bottle used while expressing. If the baby does not nurse properly and requires the mother's milk, she may express milk normally into a bottle to feed the baby, though preferably she should express only a small amount at a time.
