The Reverend Aisoli Iuli's call followed the discovery of a second dead abandoned baby in less than a month.
Reverend Iuli said a place where mothers can bring babies and abandon them anonymously in a safe place to be found and cared for has to be done.
He told the Samoa Observer newspaper the abandonment of babies happens in other parts of the world, but it is how it is addressed that matters.
"Women will go to great lengths to save face, and shame motivates the inclination to hide and murder the baby by abandonment."
Rev Iuli said the discoveries demanded a response.
The minister said the government should also consider the need to have more preventive initiatives set up, so mothers don't abandon their babies at all.