Police said the stampede occurred at one of the gates into the ceremony grounds.
“There are people who have died and others have been taken to hospital. About three of them, we can say,” a senior police officer told Capital FM News.
President Mwai Kibaki was the chief guest at the ceremony and was present at the venue when the incident occurred.
There was tight security at the venue, with each person being screened at all the gates before being allowed in causing delays.
“There was a stampede, some people got anxious and started pushing each other and caused a stampede. We have several others who have been wounded,” the officer said.
Nairobi Deputy Provincial Police chief Moses Nyakwama could not give the casualty figures, saying he had not received a proper report of the incident.
More than 2,000 officers were graduating.
Last week, there was a similar parade for 1,500 regular police officers at the police training college in Kiganjo.