Only if the baby is Rh positive. If Rh-, then no shot needed.
Interestingly, there are also often some reactions to babies who are a different blood type with other antigens (ABO and other than ABO), although there are no shots that can be given as far as I know as it could be lethal. Sometimes the introduction of A and B antigens into a type O mum may cause some reaction as well during pregnancy (the placental barrier is not hard and some foetal cells are present in mum's bloodstream during pregnancy) and which typically will also occur during delivery.
Often these babies may be a bit jaundiced if not rejected and carried to term, and they can just bake them under lights a bit to right them
The whole blood type thing is a very strange and wacky world, LOL...
Peace & blessings
Bound by conventions, people tend to reach for what is easy.
Here we must be unafraid of what is difficult.
For all living beings in nature must unfold in their particular way
and become themselves despite all opposition.
-- Rainer Maria Rilke