The Scottish Government had proposed Ms Sturgeon, who is also a Glasgow MSP, should speak at Glasgow's annual State of the Economy Conference.
However, the offer was rebuffed by the council in favour of an invite to former chancellor Alistair Darling.
The move has led the SNP to accuse the city's Labour administration of using the event as part of its anti-independence campaign.
Last night the city council dismissed the claim and said it had initially offered the role of keynote speaker to Finance Minister John Swinney.
It said Mr Darling, who as well as his role as a backbench Labour MP heads the UK Better Together campaign, was invited to speak after Mr Swinney's office said he was unable to attend.
The offer of Ms Sturgeon as a replacement was knocked back, with one source claiming: "We'll not be having the Scottish Government determine who speaks in a conference in Glasgow, organised by Glasgow and about Glasgow."
A council spokesman said: "We haven't snubbed anyone. We wanted the Scottish Government's Finance Secretary to speak at our financial conference, but he was unable to attend.