Officers responded to reports of a disturbance near the 500 block of Greens Road around 1:30 p.m, according to the Houston Police Department.
The witness said a man with a handgun was knocking and kicking their door.
Officers arrived to find him walking at a nearby park.
Police said they pursued him after he refused to stop and started running.
According to HPD, he twice went for a weapon from the waistband of his pants. That was when one of the officers opened fire at the suspect.
None of the shots hit the suspect, who later surrendered to officers. Police said he had cocaine on him.
Investigators say the suspect is wanted for a drug possession charge in Mississippi.
Police said the officer, who is an 11-year veteran of HPD, has been placed on administrative leave.