People started pushing through a passage in the Freedom City Mall just after clocks struck midnight, the force said.
“Very many people got stuck as they were entering in large numbers to see fireworks. In doing so, many people suffocated to death. So far eleven people are confirmed dead,” the police statement read.
People had been celebrating the New Year at the mall which is on a highway linking Kampala to Entebbe airport.
One eyewitness explained that people - including his friend - suffocated after getting caught between crowds that were moving in opposing directions.
Big gatherings for New Year's Eve were allowed for the first time since the start of the Covid-19 pandemic.
Kampala police said people had attended a concert at Freedom City Mall in large numbers.
A crowd surge was said to occurred when partygoers tried to head back inside - having gone outdoors to see the midnight fireworks.
Five people - described as "mostly children, juveniles" - were said to have been killed after being stepped on.
The death toll was later put at eleven after a number of people were taken to hospital.
An eyewitness, Ramadhan Aphongo, told local broadcaster NTV that a friend was among the victims: "She was enjoying, she was having fun, but due to loss of breath... eventually she died."
An investigation is under way.
