Excerpt: According to the Academy of Breastfeeding Medicine (ABM) "it is unlikely that the intact nanoparticle or mRNA would transfer into human milk" and "in the unlikely event that mRNA is present in milk, it would be expected to be digested by the child and would be unlikely to have any biological effects." For now, lactating women are asked to assess their own risks for the virus versus the benefits of vaccination. Additionally, we know that milk cannot transmit the virus, therefore human milk donors who receive the vaccine will be permitted to continue donating. WHO does not recommend discontinuing breastfeeding after vaccination.
Please see the links to organizations' statements regarding the vaccine.
AAP Statement, MFM Statement, CDC Statement