Two of the Uighurs were shot dead and the third was injured, the local government said.
Earlier reports said the three Uighurs were trying to kill passersby near the Urumqi Women and Children's Hospital.
A Uighur bystander and a policeman were also injured in the clash, the report said.
Thousands of armed riot police remain in Urumqi following some of the worst ethnic violence for decades in China.
More than 180 people have died and at least 1,700 have been injured in rioting and ethnic clashes since July 5, with about two-thirds of the victims from the majority Han Chinese ethnic group, according to government reports.
Uighur exile groups claim that up to 800 people have died in the violence, many of them Uighurs shot or beaten to death by police.