After fireworks outside the Freedom City mall in Kampala, "a stampede ensued, resulting in the instant deaths of five people and injuries to several others," national police spokesman Luke Owoyesigyire said.
Four others died on their way to hospital "largely due to suffocation."
"Emergency responders arrived on the scene and transported the injured individuals to the hospital, where nine were confirmed dead," said Owoyesigyire.
"Most of the dead were juveniles, ages 10, 11 14 and 20," Kampala police spokesman Patrick Onyango told AFP.
"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 nine people are confirmed dead," the police statement read.
People started pushing through a passage in the Freedom City Mall just after clocks struck midnight, the force said.
People had been celebrating the New Year at the mall which is on a highway linking Kampala to Entebbe airport.
One of the survivors, businesswoman Sylvia Nakalema, said the stampede started "when we went to view the fireworks on the platform and while returning downstairs".
"There was a huge crowd. People begun pushing each other for space leading some to fall and the stampede ensued," she said.
"Children were crying and there was chaos.
"I survived because I was pushed in a corner by the crowd," said the 27-year-old.
"I felt losing breath but I stayed put since I had no exit until the situation calmed down but some people were already lying down gasping for breath."
This report contains data sourced from Reuters and Agence France-Presse.