The scheme is part of Scotland's largest ever vaccination programme and should have begun at city primary schools on Wednesday.
But parents at Glendale Primary in Pollokshields, which has a large number of Muslim children who cannot use pig products for religious reasons, complained.
The scheme is now on hold in the city, although it will go ahead as planned in other health boards.
A spokeswoman for Glasgow City Council said: "We asked for a delay to the start of the programme in our schools to allow for additional information regarding the programme to be sent to families taking part."
The vaccine is being offered for the first time to every child in Scotland aged two and three. Previously only children in "at risk" groups were offered the protection.
Around 120,000 children in Scotland, including 100,000 primary pupils, will be offered the Fluenz nasal spray, which health bosses claim is the most effective available.
Dr Syed Ahmed, consultant in public health medicine at NHS Greater Glasgow and Clyde (NHSGGC), said: "We want to point out to parents and carers that the nasal spray vaccine contains a tiny amount of gelatine of pork origin used during the manufacturing process."
He said gelatine was commonly used in the manufacture of medicines and the trace in the finished nasal spray was a "completely changed substance".
NHSGGC, whose area contains the overwhelming majority of Scotland's Muslims, said it had postponed the vaccinations "following concerns raised by a small number of parents".
The health board added that, in 2001, 100 Islamic scholars had agreed pork gelatine was permissible within a vaccine so there had been no need for advance publicity.
The city council moved to halt the programme within its schools after the complaints were made, with children given letters last night informing them of the situation.
It will restart next week, with parents given the choice of an injection which does not contain the gelatine product.