The brightly coloured life-sized Clydesdale horse which was pained by a local artist was placed at Chatelherault in Hamilton as part of an exhibition by Ready Steady Gallop.
The group were planning to showcase the 'herd of horses' for the next nine weeks in streets and open spaces around the town but they have had to remove one from the trail because of vandals.
They hoped the arts exhibition would bring visitors to the centre of Hamilton over the summer and raise money for the Kilbride Hospice.
Hamilton North and East councillor Monica Lennon said: "Everyone is shocked and angered by what has happened.
"The police are following a positive line of enquiry and CCTV footage is helping with this.
"I know the community will get behind Ready Steady Gallop even more now so let's all pull together to make the project a big success for Hamilton."
Gareth Walker, BID manager, added: "We hope the people of Hamilton and visitors to the area enjoy viewing all of the other great pieces of art placed across the trail.
"Whilst disappointed by the weekend's vandalism, we don't want people to be disheartened, so are calling for the people of Scotland to get behind this project and ensure the remaining sculptures are seen by as many as possible prior to the auction in September.
"All proceeds from the auction will be donated to the Kilbryde Hospice appeal."
Gerry Campbell, general manager of South Lanarkshire Leisure and Culture, said: "This horse had quickly become a very popular attraction at Chatelherault, especially among families taking their kids there to enjoy the facilities at the park.
"It's very sad that a few mindless individuals think it is OK to ruin the fun enjoyed by so many others. Hopefully the police investigation will be successful in tracking down the culprits.
"We will do what we can to support any effort to replace the horse."