The local authority says a number of trees around the district have been attacked.
"Regrettably there have been a number of incidents of vandalism and tampering with the Christmas trees in the city centre since they were erected last week," a council spokesperson said, adding, "a number of incidents have been reported of damage to baubles and people climbing and crawling inside the trees."
The council is warning those responsible that the behaviour is dangerous and potentially criminal.
"As well as the obvious dangers this represents criminal damage and the PSNI, Community Safety Wardens and CCTV operators are keeping a close eye on Guildhall Square and Waterloo Place in particular.
"The decorations are there for everyone to enjoy so we would appreciate if people respect them and report any incidents of vandalism you experience to the PSNI," the spokesperson said.