The local authority plans to unveil this week the report on the financial ramifications of a Yes vote in next year's poll. It comes three months after the authority said it was due to be made public.
But the move comes just weeks before the by-election in Govan prompted by the death of the SNP's former leader on the council, Allison Hunter.
Her party has now called on council chief executive George Black to delay publishing the report, citing a potential breach of the Local Government Act 1986.
This bans authorities from releasing any publicity on controversial issues between the notice of an election and polling day.
They point to a decision to pulp tens of thousands of copies of the council's Glasgow Magazine after an article in council leader Gordon Matheson's name attacked Finance Secretary John Swinney for the council's financial settlement just weeks before the Holyrood election in 2011.
The SNP also point to an announcement on graduate jobs, a week before a by-election last year in Hillhead, which has a dense population of students.
The report follows a motion earlier this year by Mr Matheson claiming that as Scottish independence could have a significant impact on the economic environment "it behoves that council examines how independence would affect its ability to provide services, should Scotland secede from the United Kingdom".
Mr Black has denied the report will be political and said it is a "professional assessment [by officers] of the financial impact on the council in the event of Scotland becoming independent".
He also said as the report has already been on hold since June to take on board "significant briefings" from the Scottish Government he does not "consider that a further delay is required as a result of the Govan By-Election."
But the SNP's leader on the council, Graeme Hendry, said he was "significantly concerned" about the potential contentious nature of the report and the impact it could have on voters.
In a letter he said: "If, as seems possible, the plans to launch the first council report on the financial implications of independence are to be published prior to the by-election, then I suggest that this could be regarded as being highly politically contentious.
"We should all ensure that the election period is not unduly affected by council announcements and publications which could influence the minds of voters in Govan.
"Given this, I am asking that you will confirm this piece of work and other work which may be particularly politically contentious are not published by the council prior to the by-election."
He said: "For months the council has refused to answer the most basic questions on how this report will be completed, so to now decide to publish it during a by-election period is extremely ill-judged and may well break their own rules."
Mr Matheson said: "The SNP is scared of Glaswegians thinking about the reality of separation. A pro-independence party that doesn't want to talk about its only policy has lost all confidence in its case. That is why it is more interested in a by-election than the future of Glasgow's economy and the well-being of its people."