The city council has installed a bus gate at Nelson Mandela Place, which will result in around 800 cars each day being banned from the north side of the historic square.
Roads bosses say the move to allow only buses and taxis to use the north side will cut congestion and vehicle pollution in the area.
But Neil Greig of the Institute of Advanced Motorists (IAM) has warned diverting so many vehicles up Hope Street, to Cowcaddens Road and down North Hanover Street will cause chaos in the city centre.
He said: "This is a major change. It is inevitable there is going to be more traffic sitting in the city centre.
"Motorists have been using this route for a long time but it is now going to be bus and taxis only.
"People will be looking around for the diversion and that will lead to extra congestion in an area which is already congested."
Mr Greig also warned air quality is likely to be affected along the diversion route as a result of so many extra vehicles.
And he called for the council to introduce tighter controls on traffic management in the city centre.
The IAM boss said: "There are skips parked by the side of the road, scaffolding extended into the road and deliveries being made in the wrong place.
"The council has to be more high profile and active to keep traffic moving."
Evening Times readers who posted on our Facebook page were also not impressed by the George Square car ban.
Michael Man wrote: "I don't think it's a case of cars causing heavy traffic. If anything, I think buses cause all the tailbacks."
Gerry Gaffney posted: "The traffic in the rest of the town is bad enough as it is without diverting thousands of new cars through it."
Kirsteen Rafferty Allan said: "The safest blue badge parking spaces for me are at Queen Street Station, where I don't have to worry about other cars parking behind me and I can safely get my chair in and out of the car.
"Disgraceful. It will be much easier for everyone to use shopping centres. They have Shop Mobility as well as easy parking."
But Colin Chievely from Glasgow posted: "Great stuff GCC. I applaud this.
"For far too long have we had to put up with motorists clogging up our wonderful city centre - and far too long have we kowtowed to the motoring lobby in this city.
"Making George Square safer for pedestrians and cyclists and easier for public transport is the right thing to do for the citizens and visitors to our fine city.
"Motorists need to realise that many of them are the cause of congestion in Glasgow, and rather than moan about not being able to drive through the city should look at how they can change their behaviour to make Glasgow a better place for everyone."
A council spokesman said: "One of the aims of the bus gate is to reduce the number of vehicles travelling through the city centre while improving provision for public transport.
"This will reduce both congestion and pollution - making the city centre a more attractive destination.
"Restrictions to traffic through Nelson Mandela Place have been in place on a number of occasions during works by utility companies.
"Traffic monitoring at these times has indicated no significant issues regarding increased congestion in the city centre."