The unit on Byres Road went offline in September last year and no data has been recorded since then.
It means that potentially life-threatening levels of cancer-causing pollutants may not have been picked up, putting vulnerable people's lives at risk.
Glasgow City Council is taking legal action against the supplier who has failed to repair the unit.
The revelation follows the news that more than 300 people are being killed every year in Glasgow as a result of air pollution - higher than any other city in Scotland.
As reported in the Evening Times last week, campaigners claim air pollution is Scotland's biggest environmental health threat, killing ten times the number of people that die in traffic accidents.
Across the city levels of deadly pollutants are regularly breaking Scottish standards.
Last year, the Byres Road unit recorded levels of one type of air pollution higher than the limit, leading to fears that the broken monitor might have missed hazardous levels of another type - the deadly particulate pollution it failed to record.
Particulate pollution - caused by traffic - is particularly dangerous to children, the elderly and those with heart and lung conditions.
Local councillor Martha Wardrop said air quality was an "ongoing concern" for the community.
And the problem jars with efforts by the local residents to improve the area and boost its appeal for pedestrians and cyclists.
She said: "Pollution is an ongoing concern for the community and air quality has been a priority for local residents.
"I have come across some people who have just stayed indoors on very hot days.
"If they have got a lung condition it is difficult to walk around in the heat anyway."
Emilia Hanna, from environmental charity Friends of the Earth, said it was disappointing that the Byres Road monitor had been offline for so long.
She said: "Particulates are cancer-causing pollutants caused by traffic, which we know is a problem in this area.
"Levels of particulates in Glasgow are so high that they are breaking Scottish standards, so it is really important that particulates are monitored and kept under control."
A spokesman from Glasgow City Council said: "As the unit is still under warranty we sought to have our supplier repair it as soon as possible.
"Unfortunately, this did not happen and we are currently seeking to take legal action against the supplier."