The giant glass jar, placed outside the city's Glasgow's Gallery of Modern Art, was smashed and its contents taken.
Designed by artist Caio Locke, it was entitled Endless Carnival and contained two painted merry-go-round horses.
It was one of 50 created to raise funds for Save the Children and Roald Dahl's Marvellous Children's Charity.
The Glasgow jar, which was more than 4ft tall (1.28m), has now been removed from the trail.
Personalities from across the globe, including Steven Spielberg, Prof Stephen Hawking, Simon Cowell, the Duchess of Cornwall and BFG actor Mark Rylance, were invited to help design a jar for the fundraising drive. The sculptures were then created by a specialist design company.
Most of the dream jars are displayed in London but Glasgow, Birmingham, Cardiff and Cheshire are also taking part.
Artist Caio Locke said his jar evoked the enduring magic of the fairground carousel: "My dream is a carnival that never ends, with magical horses designed to keep the merry-go-round forever turning."
Natasha Parker from Save the Children said: "We are incredibly disappointed to learn that Ciao Locke's The Endless Carnival Dream Jar which was a beautiful and unique piece of art, has been taken from the city centre and will sadly no longer be a part of The BFG Dream Jar Trail.
"It was set to raise thousands for Save the Children via the live online auction at www.paddle8.com/bfg to help vulnerable children around the world get the chance to make their dreams come true."
A spokesman for Glasgow City Council said: "We were approached by the organiser of this project and asked to find a suitable location in the city.
"It's deeply disappointing that an artwork intended to help raise money for vulnerable children has been vandalised.
"If anyone has any information on who is responsible then we urge them to contact the police."
A BFG Dream Jar artwork that was to be auctioned for charity has been vandalised after going on display in Glasgow.