In a letter to all 500 Catholic churches in Scotland bishops will say that "on serious issues some politicians who profess a Catholic faith remain silent - or even surrender - in the face of grave ethical injustice."
Jim Murphy has been vocal about his Catholic faith in the past but has gone against Church teachings on several parliamentary votes.
In February 2013 the Labour candidate for East Renfrewshire voted in favour of gay marriage in England and Wales despite a vocal campaign by the Church against the move.
At the time he said he had received pressure from other Catholics because of his decision: "Sadly one or two constituents have been personally abusive.
"They have chosen to question my faith and my right to simultaneously be a Catholic and vote for this change.
"In our democracy people have that right but the personal abuse is something I wouldn't have expected from people who profess to share a faith with me.
"In fact those who were most abusive were lay people of faith who seemed to believe they were the keeper of my conscience."
He added: "Some of the MPs voting against the plans say that same-sex marriage is incompatible because the purpose of marriage is to bring up children.
"I agree that this is an important part of being married and is central to the Church's teaching and definition of religious marriage but it cannot be the legal purpose of marriage."
Mr Murphy was elected leader of the Scottish Labour Party in December 2014.
According to Christian Concern the former MP voted against a bill that would have required independent advice be made available to women requesting an abortion.
Jim Murphy did not attend parliament to vote on the issue of so called 'three parent babies'.
The bill to allow mitochondrial donation with the aim halting the inheritance of mitochondrial disease was eventually passed.
The Christian Concern website says Mr Murphy casted five 'bad votes' in the last parliament which it claims went against Christian teachings.