The most current and reliable information can be found on the CDC website Interim Guidance on Breastfeeding for a Mother Confirmed or Under Investigation for COVID-19.
Breastfeeding is the preferred method of infant feeding in most cases and this decision should be made by the family in consult with their health care provider if there are health concerns. It appears at this time that the primary concern is not whether the virus can be transmitted through the breastmilk, but rather whether a mother who has tested positive for the virus can then transmit it during the period in which she is breastfeeding.
In this case it would be through droplet transmission such as with a cough. Mothers who have confirmed COVID-19 or those with symptoms of fever, cough or other illness should take all possible precautions so as not to expose their infant. Washing your hands before touching your infant and wearing a face mask if possible, while breastfeeding are two of those recommendations.
If you decide to express breast milk with a manual or electric breast pump, you should wash your hands before touching any pump or bottle parts and follow recommendations for proper pump cleaning after each use. You may also consider having someone who is not sick feed your expressed breast milk to the infant.
Although there are no data reporting the transmission of the virus through breastmilk, it is not possible to determine if COVID-19 can be transmitted due to the limited number of cases.
This information was gathered from the American College of Obstetrics & Gynecology and the CDC.