Police Scotland said the crash in Hyndland Road, in the west end of the city, happened at about 3.45pm on Tuesday.
A statement read: “Seven people have been taken to hospital for treatment, and to be assessed, following the incident and the driver has been assessed by paramedics at the scene.
“Officers remain in attendance and enquiries are ongoing into the incident which is being treated as a road traffic collision.
“Hyndland Road remains closed and members of the public are urged to avoid the area.
The Scottish Fire and Rescue Service (SFRS) has also confirmed it was called to the incident.
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Glasgow City Council said Hyndland Road was shut between Clarence Drive and Novar Drive.
The local authority said: “Road users are advised to avoid the area and consider alternative routes.”
