Emergency services rushed to the scene at around 8.40am on the A814 Clydeside Expressway at Finnieston and the youngsters were taken to the nearby Royal Hospital for Sick Children at Yorkhill for treatment.
The adults were also taken by ambulance to the Western Infirmary.
Three cars were involved in the crash including a private hire silver Skoda taxi which was hit from behind and ended up on a grass verge.
A blue Mazda 5 and a red Peugeot blocked the road causing major tailbacks at the busiest time of the morning.
Motorists were hit with major delays on their way into the city centre and the road was closed.
Police were at the scene diverting traffic while crews removed the damaged vehicles and emergency services treated the injured at the scene.
Firefighters were also called to scene as a precaution in case the injured had to be cut from their vehicles.
One lane on the Eastbound carriageway reopened shortly before 10am but drivers were being advised to avoid the area if possible.
The victims are still in hospital and the extent of their injuries are not yet known but they are not thought to be serious.
A Police Scotland spokeswoman said: “Around 8.40am we received a report of a three-vehicle collision on the Clydeside Expressway just before the Finnieston cut off.
“Emergency services attended and four adults were conveyed to the Western Infirmary in Glasgow and two children were taken to Yorkhill as a precaution.
“They condition is not yet known but the injuries are not believed to be serious. One lane was closed for a short time but has now been reopened.
“The road was closed to clear the vehicles.”
As shown in our exclusive photos of the crash, heavy rain overnight had made road conditions wet and difficult for drivers.