The incident took place late on Sunday in a village near the city of Kashgar.
The government-run regional news portal said police trying to make arrests were attacked by people armed with explosive devices and knives. Police shot dead 14 people, with two policemen also killed.
Xinjiang, home to the Muslim Uighur minority group, sees sporadic clashes.
The government traditionally blames extremists for the violence, while Uighur activists point to ethnic tensions and tight Chinese control as triggers for violence.
Verifying reports from the region is difficult because the information flow out of Xinjiang is tightly controlled.
The report, on the official Tianshan news portal, said two people were also arrested.
Last month, state media reported nine civilians and two police were killed in an attack on a police station near Kashgar.
In late October, five people were killed when a car ploughed into a crowd and then burst into flames in Beijing's Tiananmen Square.
Beijing called the incident a terrorist attack inspired by Xinjiang-linked extremists. Three people who died inside the car were identified by police as Xinjiang Uighurs.