The victim managed to run off towards George Square, where he phoned for the police and an ambulance.
Under the scheme, George Square and Upper Dundas Street will be redeveloped before the Commonwealth Games in 2014.
Organisers, the Scrap Trident Coalition, led campaigners through Glasgow city centre before holding a rally in George Square.
An online petition has been started, calling for George Square to be restored to "its former grassy glory".
Glasgow's George Square is to receive a revamp in time for the city's hosting of the 2014 Commonwealth Games.
In Glasgow, several hundred people gathered in central George Square, celebrating to a soundtrack of rock music and bagpipes.
William Burdett Coutts, Assembly director, said he was excited about George Square because it is a "very interesting environment".
BBC: The Assembly Theatre Fringe venue to leave 30-year home
Designs by six short-listed companies taking part in the international competition to redevelop George Square in Glasgow have gone on public display.
The leader of Glasgow City Council is being investigated by police over his handling of the controversial George Square revamp.
The Assembly Theatre is to move from its home in George Street, where it has been for 30 years, to George Square.
BBC: The Assembly Theatre Fringe venue to leave 30-year home
The complaint made to the police relates to the council's decision in January to drop plans for a radical redesign of George Square.
He will also take over the George Square lecture theatre as a 480-seat space, along with two other rooms holding 200 people each.
BBC: The Assembly Theatre Fringe venue to leave 30-year home
Glasgow City Council leader Gordon Matheson said the calibre of the companies vying for the work underlined the "iconic" status of George Square.
As part of its continuing campaign, FAC applied to Glasgow City Council to stage a rally in George Square followed by a street parade.
He added that he would be running about five theatre spaces, including two Spiegeltents in George Square, with seating for 450 and 200 people.
BBC: The Assembly Theatre Fringe venue to leave 30-year home
Police say up to 1, 000 protesters were at the march, which is part of a weekend of events with workshops remaining in George Square on Sunday.
The teenager is in a stable condition in hospital after he was shot in Great George Square, in the city's Chinatown, at about 21:30 BST on Friday.
Speaking in George Square, Mr Smith said the priority should be fair taxation and a living wage, investment in quality jobs, strong trade unions and employment rights.
The proposals will see 13 monuments in George Square - excluding the cenotaph - temporarily relocated to other parts of the city while redevelopment work is under way.
But for the second year in a row, there were no official celebrations at midnight in Glasgow - with the city's Hogmanayday event in George Square ending at 22:00.
In Glasgow, 25, 000 turned out for its celebrations in George Square, while in Aberdeen 40, 000 people watched Scottish acts Deacon Blue, Hue and Cry and Fame Academy winner David Sneddon.
BBC: Celebrations were toned down in the wake of the tsunami
With action scenes shot in Glasgow's George Square and starring Brad Pitt, it has been adapted from Max Brooks' 2006 book World War Z: An Oral History of the Zombie War.
An online petition, calling for George Square to be restored to "its former grassy glory", also attracted thousands of supporters and a rally against the revamp was being planned for 2 February.
BBC: George Square redesign: Council drops radical revamp plan
The council will close the centre of the city to traffic for the day and are considering erecting two giant screens in George Square so visitors and locals can watch the action live.
Mr Burdett Coutts told the BBC Scotland news website although he would be putting a bid in to return to the George Street premises he said he hoped the Assembly Theatre would be in George Square "long term".
BBC: The Assembly Theatre Fringe venue to leave 30-year home
The SNP group on Glasgow City Council has lodged a motion calling on the local authority to "invite Audit Scotland to investigate whether councillors unduly influenced the procurement process in the case of the George Square redevelopment procurement process".
The motion calls for "early action to commission a statue equal in quality to that which stands in St George's Square in his home town".
At the last count, five separate events are being held at venues ranging from the Lloyd George statue in Parliament Square to the National Liberal Club.
Images of Alfred Hitchcock fleeing from the pigeons on Trafalgar Square, George Orwell installing CCTV cameras and the Mayor of London Boris Johnson polishing the shoes of his predecessor Ken Livingstone are among the tongue-in-cheek caricatures that welcome you.
The buses will then travel down Callaghan Square and Lloyd George Avenue, heading to Cardiff Bay.
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