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 square.
Roads bosses say the move to allow only buses and taxis to use the north side will cut congestion and pollution.
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.
"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.
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 congestion and pollution - making the city centre a more attractive destination."