Human milk is not included in the prohibition of mixing meat and (animal) milk, and would therefore fall into the category of "pareve." The rabbis, however, taught us that we shouldn't mix mother's milk with meat because of "mar'it ayin": someone seeing the mixture might think that this is a forbidden combination of milk and meat.

Since it is not dairy, it's not a problem if a drop of breast milk accidentally falls into meat or if a bottle used for breast milk is washed with meat dishes.

All the best,

Rochel Chein for Chabad.org