Tony Danker said he had not met a business leader who thinks "this is a really front-of-mind issue".
It came as he issued a plea to the First Minister to work better with business leaders, insisting there "isn't enough" dialogue.
Sturgeon wants to hold a referendum in October next year, but the UK Government has refused to agree to this.
A Supreme Court battle is due to take place next month over whether Holyrood has the power to legislate for another vote without UK approval.
Asked if it was the right time for the Scottish Government to be pushing ahead with plans for another vote, Danker said: "I have to tell you, I really don't think about it, and the members that I speak to here in Scotland aren't talking about it.
"People are talking about two questions only. One, what are we going to do about the short-term energy and economic crisis?
"And two, how on earth do we in Scotland or we in the UK grow our economy? By the way, that will be doubly important now that we're about to take out a lot of government debt.
"The only way you can take out that amount of government debt is because you've got a credible plan to repay it.
"So I understand why it's such a dominant political issue, but it's just not an issue for business leaders right now. They are focused on almost everything else."
Danker, who was speaking to The Scotsman before news emerged of the Queen's death, said the issue of a second independence referendum "hasn't come up" in conversations with business leaders.
Asked if he thought constitutional uncertainty in Scotland had any impact on the business community, he said: "I understand why you're asking it, and if you'd asked me about it a few years ago, of course it would have been top of mind for everybody.
"I haven't met a business leader, and I don't think I'll meet one today, who thinks this is a really front-of-mind issue."
Elsewhere, Danker, the director-general of the CBI, backed moves to push ahead with more oil and gas exploration licenses.
Secretary of state for energy Jacob Rees-Mogg confirmed on Thursday the UK Government would support more than 100 licences for companies to explore for more fossil fuels in the North Sea, as well as lifting the moratorium on shale gas drilling in England.
But environmental campaigners, led by Greenpeace, have threatened legal action over the plans, which have been described as “denying the reality of the climate emergency”.
Danker said it was "realistic and pragmatic" to go ahead with extra exploration licences, but stressed "plan A" was still moving to clean energy.
He said nobody doubted the critical role that oil and gas would play in the transition, adding: “And so yes, it’s completely understandable and I would be supportive of those actions, because we’re trying to create a transition here.
"The only thing I would say is that shouldn’t be plan A. Plan A is still Britain becoming, in fact, and it’s at the heart of our growth story, the world's leading country for clean energy.”
Danker said oil and gas was not the long-term answer.
A Scottish Government spokesman said: “There is a democratic mandate from the people of Scotland for an independence referendum.
"The UK economy already delivers low productivity, stagnant wages and high inequality compared to many of our EU neighbours, and its relative performance is likely to deteriorate further as the negative effects of Brexit become more apparent.
“In addition to giving the opportunity to re-join the EU and a market seven times bigger than the UK, the full powers of independence would enable the creation of an economy that works better for all people and businesses, allowing Scotland to match the higher productivity, higher incomes and lower inequality achieved by comparable independent European countries.”