Most viruses penetrate the body somewhere--gut, respiratory tract,
other mucous membranes.  There is then a short period of "viremia"
when the virus travels in the blood to wherever it's going, in the
case of hand foot and mouth disease, to the hands feet and mouth.
During that short period of time (often hours), when the virus is in
the blood, it could conceivably be passed on through the milk.  But
once it is out of the blood no, unless it multiplies in the breast
cells, which is pretty unlikely.

However, the viremia occurs *before* the mother has clinical
manifestations of the disease.  This is, by the way, an unusual
illness in adults, and if the baby got this, he more likely got it
from another child than the mother.

This all means, of course, that the mother should *not* stop
breastfeeding if she has hand foot and mouth disease.

Jack Newman, MD, FRCPC