Officials said officers were called to Richmond near Hillcroft shortly before 3 a.m. regarding the crash and found only one vehicle with one person in it.
Officers say another car that was involved had left the scene.
At one point, officers checked on the man in the driver's seat, who HPD said got out of the car with a gun in his hand. Officers then commanded him to put the weapon down, but officials said the man did not comply.
HPD said the man then turned toward the officers, who opened fire and hit the man at least once.
The suspect was taken to the hospital with non-life-threatening injuries.
None of the officers were hurt, HPD said.
Officials said they spoke with witnesses who saw the crash that occurred before the shooting and are searching for who may have been involved.