He is accused of shooting and killing his passenger, 45-year-old Hyun Kim, in the early-morning hours of June 1 on Interstate 25 near University Blvd. in Denver.
Police said Hancock shot Kim multiple times after getting into some kind of altercation inside the vehicle.
According to a statement of probable cause provided by Denver police, the driver told a witness that Kim tried to attack Hancock and "the driver shot him."
The witness called 911 and passed the phone to Hancock, who identified himself to the dispatcher, the report said.
When officers arrived on scene, they found Kim lying on the floorboard of the front passenger seat. They then attempted to perform CPR on the passenger, but Kim was pronounced dead at the hospital.
While still at the scene, police removed a semiautomatic pistol from Hancock's right waistband and located "10 spent 40 caliber cartridges on the left shoulder of Interstate 25 near University Blvd," the police document read.
Uber confirmed that the incident appears to be associated with an on-app trip and that Hancock has been an Uber driver for nearly three years. The company said it has since removed Hancock from the app.