The environmental campaigners fear plans for the zone due to be unveiled by the city council on Friday will include only limited restrictions on buses when it comes into force at the end of December.
The concerns came as ministers announced 95.5 per cent backing for LEZs in a consultation on their planned introduction to Scotland's four largest cities by 2020.
Edinburgh is keen to be among the first after Glasgow.
Glasgow intends to ban the most polluting buses first, but this may take some time to implement.
Friends of the Earth Scotland air pollution campaigner Emilia Hanna told The Scotsman: “The Scottish Government has committed to delivering LEZs to tackle Scotland’s urban air pollution crisis.
"But conversations we have had with Transport Scotland officials have rung major alarm bells about lack of ambition for the first zone in Glasgow, which may do as little as requiring only a small portion of buses to achieve clean emission standards.
"Such a zone would not deliver the desperately-needed clean air Glasgow residents were legally supposed to have had by 2010, and will make a mockery of the Scottish Government’s commitment to tackle air pollution.
"We urge Glasgow councillors to make sure the city’s LEZ is fit for purpose when they debate it next week."
Anna Richardson, the council's convener for sustainability and carbon reduction, said: “In establishing the first LEZ in Scotland we are making cleaner air a priority.
"It is essential that the phasing of this zone is done at a robust yet realistic pace, that will bring about the air quality improvements we need without having a detrimental impact on public transport or Glasgow’s economy and businesses.
"Our LEZ will cover all vehicle types once fully implemented.”
Mr Yousaf said: “I am delighted to see real progress being made by Glasgow City Council with their proposals for Scotland’s first LEZ to be in place by the end of 2018.
"As with the vast majority of LEZ across Europe a lead-in time is a sensible measure.“Transport Scotland and Glasgow City Council are engaging closely with the bus industry on the necessary lead-in times for transition and we are committed to ensuring buses remain part of the solution to improving air quality."
Mr Yousaf said there had been 95.5 per cent backing for the principle of LEZs to help improve air quality among the 967 responses to the Scottish Government consultation.
Nearly two in three - 62.3 per cent - agreed that only vehicles with the cleanest engines should be allowed in LEZs.
These are Euro 6 for diesel cars, introduced only four years ago, Euro 4 for petrol cars, introduced in 2005, and Euro VI for buses.
However, responses to the consultation, Building Scotland’s Low Emission Zones, appeared to show only minority support for banning vehicles from entering LEZs.
A road access restriction scheme was backed in some way by 42 per cent, while 28 per cent did not support it or preferred an alternative.
Mr Yousaf said: “These zones will improve air quality, tackle congestion and help improve our urban environments.
"However, it is critical this is done in a consistent manner and in partnership with local authorities, industry and regional transport partnerships.
“Local authorities should be ambitious in their LEZ designs and consider all vehicles for inclusion, with appropriate lead in times to enforcement, for both buses and private vehicles."