Sister Helen Prejean condemned what would have been the most intense spate of state-sanctioned killings since the death penalty was reintroduced 40 years.
Addressing Asa Hutchinson on Twitter, she said: "As a state official, you should not be involved in the killing of human beings. Be a statesman and a real moral leader."
The plea came too late for one of the inmates on death row.
Ledell Lee, a 51 year old convicted murderer, was executed by lethal injection on Thursday night despite last minute attempts by a defence team - who protested his innocence - to keep him alive.
Gov. @AsaHutchinson's killing spree will open many people's eyes to the injustice that is our death penalty. It's time to abolish it.
— Sister Helen Prejean (@helenprejean) April 21, 2017
JR Davis, a spokesman for the governor said: "The governor knows the right thing was done... Justice was carried out."
Three of the eight executions have subsequently been cancelled owing to court decisions; another inmate scheduled for execution has received a temporary reprieve, while three others are still set to die next week.
Based in the Louisiana city of New Orleans, the Catholic nun also wrote on Twitter: "Why do we kill people to show that killing people is wrong?"
Prejean rose to prominence during the 1990s with her book, Dead Man Walking.
Speaking with the Guardian, she said: "The Bible belt and the 'death belt' are the same belt. It's blatant.
"Religion is used to shore the death penalty up, so that officials can quote divine authority for what they are doing.
"That way religion becomes 'an eye for an eye' and killing in God's name. When you claim that, you become impervious."