It is thought to be related to possible cases of personation, where people pretend to be someone else and cast a vote, then the real person turns up.
The 10 suspect votes were cast at a variety of different polling stations across the city.
Glasgow City Council said police had been called earlier on Thursday.
Each ballot paper has an individual number attached to it, so officials will now have to sort through the ballots and attempt to find these 10 papers.
They will then be removed, and kept separately from the more than 486,000 ballot papers being counted in Glasgow.
Colin Edgar, head of communication at Glasgow City Council, said the search for the ten ballot papers "will not delay the count".
Police Scotland said any crime committed would be appropriately investigated.
A spokesman added: "Police Scotland takes the safety and security of the independence referendum extremely seriously and is working with partner agencies including local authorities to ensure the integrity of the ballot."

The advertisement shows a black, emaciated child holding a red parasol over the fair, bejewelled actress.
A group of activists, in an "open letter" to Ms Rai Bachchan, called the image "extremely objectionable".
The film star's publicist said she had been photographed without the backdrop.
"The final layout of the ad is entirely the prerogative of the creative team for a brand," Ms Rai Bachchan's publicist said in a statement, suggesting that the actress had not been involved in the final image that appeared in the advertisement for Kalyan Jewellers.
The ad featuring the 41-year-old, who is a former Miss World, appeared in a newspaper last week.
After criticism, the company issued an apology on its Facebook page. It said the advertisement was intended to portray "royalty, timeless beauty and elegance" and expressed deep regret for any inadvertent hurt caused.
The company said it had begun withdrawing the ad from its campaign.
In an open letter addressed to the film star and published on Wednesday, a group of activists expressed "dismay" at the "offensive image".
"In the advertisement you appear to be representing aristocracy from a bygone era - bejewelled, poised and relaxing while an obviously underage slave-child, very dark and emaciated, struggles to hold an oversize umbrella over your head.
"The extremely fair colour of your skin (as projected in the advertisement) contrasted with the black skin of the slave-boy is obviously a deliberate 'creative' juxtaposition by the advertising agency, and insidiously racist."
The activists said the image reminded them of "17th and 18th century colonial European portraits of white aristocracy, depicting women being waited upon by their 'black servants'" and called on the actress to dissociate herself from "this offensive image".
In India, where there is a marked preference for fair skin and skin-whitening creams and lotions are big business, many say the advertisement perpetuates the retrograde idea that fair is beautiful.
The advertisement was also criticised on social media. Author and activist Meena Kandasamy tweeted:
Officials at the referendum count in Glasgow have said they are investigating 10 cases of suspected electoral fraud at polling stations.
[NEXT_CONCEPT]
An Indian jewellery advertisement featuring top Bollywood actress Aishwarya Rai Bachchan has been withdrawn after criticism that it was "racist" and promoted child slavery.