Almost 400 ballot papers were found for the Langside ward, where Labour, the SNP and the Greens won one councillor each in a closely fought contest.
The ballot papers were from Battlefield Primary School, which was used as a polling station, but they had not been entered into the final count at the SECC the following day.
The votes were registered and scanned but not entered for the final count.
Archie Graham was elected first for Labour, followed by Susan Aitken for the SNP.
But a series of counting of second and third preference votes and eliminations of those with the fewest votes then followed before the Greens won the third seat in the ward.
The missing votes could have an impact on that result, which saw Paul Coleshill, the city's LibDems' leader, lose his seat to the Green Party's Liam Hainey, who beat him by just 80 votes in the first round of voting.
Mr Hainey was elected at stage eight, narrowly defeating the second SNP candidate Alex Hewetson by 120 votes.
The council will now ask Glasgow Sheriff Court for permission to add the votes into the calculations to see if it was enough to affect the result.
Candidates have been told of the find and told the election of Mr Graham and Ms Aitken is not in any doubt.
Any change in the Langside result would not affect the overall Glasgow result, where Labour was returned to power with 44 councillors, giving the party a majority of five.
However, the SNP is looking for a recount before the council meets next week to put the Langside result beyond any doubt.
James Dornan, MSP for Cathcart, which includes the Langside ward, said: "Glasgow City Council cannot delay. Officials must arrange a recount immediately for the sake of the affected candidates and the reputation of the competence of the council.
"Council bosses must give the people of this city guarantees that Glasgow will review its procedures to ensure this has not happened elsewhere."
A spokesman for the Scottish Green Party said: "We were delighted with the election of Liam Hainey in Langside. The uncertainty voters and councillors now face is in nobody's interest.
"We will want a full statement of the reasons for this incident, and we hope to see Liam confirmed as Green councillor for the ward so he can get on with his work representing the community."
The council said George Black, the Returning Officer, met the elected members from Langside to tell them of the error.
He has also written to all the candidates who stood in the ward and his staff have contacted them by telephone.
Mr Black told candidates: "It is my intention to enter those ballot papers into the system and rerun the calculation to ensure the result is accurate."
stewart.paterson@ eveningtimes.co.uk
