James Dornan, MSP for Glasgow Cathcart, made the comment to the Conservative MP after he replied to a video posted on Twitter about the Nationality and Borders Bill.
The controversial Bill states that Border Force officers will be able to use “reasonable force if necessary” to turn away UK asylum seekers.
Commenting on the video, Jacob Rees-Mogg said: "The bands of blighters bringing illegal entrants to Blighty will be broken up by this brilliant borders bill."
Mr Dornan replied on his private account to the MP, a practicing Catholic who is anti-abortion based on what he claims are his religious beliefs.
Dornan replied: "Hope you remember this the next time you go to confession.
“You and your cronies are already responsible for the deaths of thousands and you’re now happy to see the most desperate people in the world suffer and drown.
"If your god exists you will undoubtedly rot in hell."
Annie Wells, the Conservatives’ health spokesperson, added: "James Dornan's latest outburst is beyond the pale and serious questions need to be asked here."
Last month, Mr Dornan was criticised for falsely-accusing Lothian Buses of anti-Catholic discrimination after they were forced to cancel services on St Patrick's Day due to anti-social behaviour.
Conservative MSPs have said the SNP need to provide answers over Dornan’s comments.
Stephen Kerr, Scottish Tory convener said: "I try to avoid commenting on this particular MSP; but this latest comment is beyond the pale - the SNP need to tell us why they think it is appropriate they keep this person in their party."
Mr Kerr went onto say that Dornan has subsequently been reported to the Standards Commission for Scotland.
He added: "It is clear that he wasn't interested in adhering to the MSPs' Code of Conduct when posting this reply, which is why this post has now been reported to the Standards Commissioner."
The Standards Commission for Scotland has been contacted for comment.