The warning will be issued by CBI Director-General Carolyn Fairbairn when she also warns of the “catastrophic risks” of a no deal Brexit at a dinner attended by the First Minister.
Ms Sturgeon has made repeated calls for a Scottish-specific immigration system in the aftermath of the Brexit vote.
But Ms Fairbairn will say businesses she has spoken to say “not right now” in a speech tonight which will focus on the impact of EU withdrawal on business.
Speaking at her third CBI Scotland Annual Dinner at the Hilton Hotel in Glasgow, Ms Fairbairn will argue devolving immigration would create unwanted red tape.
Instead she will emphasise the importance of building a UK-wide post-Brexit immigration system that combines public confidence with ability to attract the people and skills companies need.
The SNP has contrasted its approach with the UK Government's “hostile” approach to immigration which, she says, risks damaging the Scottish economy.
Ms Fairbairn will acknowledge that Scotland had problems with skill shortages but will take issue Ms Sturgeon's claim that a Scottish immigration system was the answer.
“Scotland has a brilliant and talented workforce. But look at the stats, and it’s also a shrinking workforce,” Ms Fairbairn will say.
“Demographics are not in Scotland’s favour. Add Brexit uncertainty and a brain-drain to the South East and overseas and you have a potent mix of problems.”
The CBI's vision was for a system that was “open, but controlled too,” she will say.
“We are clear it must work for Scotland,” she will say. “Some have asked – do we need a devolved solution for Scotland? It’s a fair question.
“But the businesses I’ve spoken to say `not right now'. Let’s get it right for the whole UK. The better the outcome we get, the less need for variation across the UK. The less companies need worry about doubled up systems and extra red tape.”
The First Minister's spokesman said: “We are clear there is a weight of evidence that Scotland should be in control of its own immigration policy.”