Since mom herself will be back on her period soon, there's no valid, medically-proven reason that someone's menstrual cycle would cause any harm to a newborn.
During Your Period
One concern I had in particular was a bit awkward, but I needed to ask. As it turns out, the pediatrician agreed that it was unsafe and unsanitary to co-bathe with my newborn while I was on my period.
Can you bath with your baby while on your period?