Phil Gordon, a professional tree surgeon, was working in Abbey Park when the accident happened. He was taken to Leicester Royal Infirmary where he died.
Gordon represented the Green Party on Leicester City Council.
Sheila Lock, chief executive of the council, said: "We are all extremely shocked and saddened by this news, and our deepest sympathies go out to his family, his co-workers, and everyone who knew him.
"Councillor Gordon was one of our first Green councillors, and along with his then co-councillor Matt Follett brought a fresh approach into the council chamber, championing the cause of recycling both in the city and in the council.
"He was an arborist, and had been working alongside our trees and woodlands team for just over a year. He will be greatly missed by them."
The council said a book of condolence would be opened at Leicester Town Hall.
A spokesman for the Health and Safety Executive said it was investigating the incident, while a spokeswoman for Leicestershire Police said there were no suspicious circumstances surrounding the 48-year-old's death. A file was now being prepared for the coroner.