Mary McNab, held the Glasgow North East seat for Labour in a by election after Maureen Burke resigned when she became an MP in July.
However, McNab is an employee of the council and under electoral law has to resign from her job the following working day.
As the result was declared on Friday November 22 she had to quit by the following Monday.
When she failed to do so it meant she is still an employee of the council and is disqualified from being a councillor.
The unprecedented situation has led to the council going to court to establish the exact legal position.
However it means another by election will have to take place to elect a councillor for Glasgow North East.
The result last month was on a very low turnout of just 12.4%.
McNab won one of three by elections held in the city on the same day.
The party also held the Maryhill and Drumchapel Anniesland seats in the city.
Another council by election is due to take place this month in Partick East/ Kelvindale following the death of SNP councillor Kenny McLean.
Glasgow Labour Group has been contacted for comment.
A spokesperson for Glasgow City Council said: On Tuesday it became clear that the victor in the North Est by election had reigned from her employment in Glasgow City Council.
This automatically disqualified her with the effect she is no longer a councillor and a by election will need to be held.
“This is however untested legal ground and to ensure the law is being correctly interpreted we will tomorrow (Monday) begin the process of seeking a declarator from the Sheriff Principal to that effect.”
