Tory finance spokesman Murdo Fraser made the comments during First Ministers Questions at Holyrood. It follows figures last week which show Scotland's population has reached a record high. Although it was driven by immigration increases, this is lower north of border then elsewhere in the UK.
Mr Fraser said today: "Scotland has consistently attracted fewer migrants coming to live here relative to other parts of the United Kingdom when you look at our population share.
"Why does the First Minister think that after ten years of SNP Government Scotland is a relatively unattractive place for immigrants to come?"
The claims prompted an angry response from the First Minister.
"What a disgraceful thing - what an utterly disgraceful thing," Ms Sturgeon said.
"For a member of this Parliament to stand up in this chamber and describe his own country as an unattractive place to live.
"Murdo Fraser hang your head in shame."
Ms Sturgeon added: "I remember the days, and they are becoming dark and distant days, when Murdo Fraser used to be a serious politician. Now it seems he just aspires to be a figure of fun in this chamber.
The First MInister said Scotland must encourage people to come and live her, but insisted more migrants settle in London and the South-east because fo geography.
"The real question is not the one that Murdo Fraser posed, the real question is this: Are we going to make sure over the next few years that we continue to have the ability to attract people to come to live in Scotland or are we going to allow narrow-minded Tories to put barriers in the way of that."