A spokeswoman for Glasgow City Council said there was damage to the exterior wall of the historic administrative headquarters of the city's council, but that no-one had been injured during the incident.
The accident happened during the shooting of a crash scene between a car and a bus on the set of a new film, Kick,
The council spokeswoman: "The vehicle has knocked down part of the wall of the chambers and obviously we will be having discussions with the production company."
Glasgow's versatility has allowed the city to accommodate a slew of Hollywood films, but now it is hosting its first Bollywood blockbuster.
As thousands crowded to the Merchant City Festival, just round the corner the scene was being set for new Indian movie Kick, starring heart-throb Salman Khan.
Cochrane Street – which in 2011 was transformed into Philadelphia's Pennsylvania Street for Brad Pitt's World War Z – was dressed as a London street for the start of 15 days of filming in Glasgow.
Although dozens of fans travelled to George Square, to try and catch a glimpse of Khan, the actor was not on set, although he is believed to have flown into Glasgow on Friday.
His co-star, Randeep Hoodah, signed autographs for fans after filming a car crash scene in the same place that hosted World War Z's zombie-filled traffic jam.
Warda Nadiadwala, wife of the film's producer, Sajid Nadiadwala, was posting Twitter updates from behind temporary fences shielding the action from passers-by.
As well as some excited tweets – "First shot at 10am in Glasgow guys finally Kick start woohooooo!" – Warda shared photographs of the action with her followers.
The stunt sequence, with Bombay Talkies actor Hoodah, involved a crash between a car and a bus with the London destination Kings Cross on the front.
Although Khan was not on set he is believed to start filming next week, and is likely to be a draw to Bollywood fans living in the city.
Glasgow is used to the attention, having recently played the backdrop for not only World War Z but also Cloud Atlas and Fast And The Furious 6.
David Tennant, Rosamund Pike and Billy Connolly have just been in the city to shoot part of What We Did On Our Holiday, also set in the English capital.
Figures for 2012 showed Glasgow's reputation as a prime location for Hollywood producers brought in £23 million for the city, with revenues up 10% on the year before.
The rise came even though the number of big names arriving in the city last year dropped compared with 2011, when Brad Pitt and Halle Berry came to town.
Glasgow's distinctive Victorian architecture and grid street design, similar to American cities such as Chicago or Philadelphia, are a draw for directors looking for a cost-effective way of filming.
Cloud Atlas saw Glasgow double not only as 1970s San Francisco but also as modern-day London as Halle Berry shot scenes near Blythswood Square, while Jim Broadbent was photographed in Anchor Lane, just off George Square.
Directors have also spoken of the willingness of the city authorities to co-operate – and how friendly local people are, despite disruption to traffic and street closures.
Glasgow is not the only Scottish location to have had a shot of Hollywood glamour: last year saw Scarlett Johansson bring movie magic to a petrol station in Wishaw for the filming of Under The Skin.
Several streets in the centre of Glasgow will be closed during the next fortnight for scenes from the Bollywood movie to be shot.
The area immediately around George Square was affected all weekend, with filming moving to other places from Monday.
A spokesman for Glasgow City Council said the impact to shoppers, commuters and local businesses would be minimal.
He said: "The filming team are making every effort to minimise the impact of the filming on businesses in the community. The streets will be carefully marshalled by filming staff and by Police Scotland during filming hours. It is important to emphasise that pedestrian access to the streets will be maintained, although routes may vary, and all businesses will remain open."