The victim, 55-year-old Prentis Robinson, was streaming video on Facebook Live when he went to the police department to complain about a family member stealing his cellphone.
He was still broadcasting when he left and was confronted by a man.
The two had an argument. In the video, shots are heard ringing out.
The footage ends with the camera falling to the ground.
The suspect, Douglas Colson, turned himself in to police on Tuesday morning.
Colson is expected to be charged with Robinson's death.
"This is a terrible incident and our thoughts are with the victim and his loved ones," a Facebook spokesperson said in a statement. "Because we cannot have known that the victim would have wanted this horrific act to be live streamed on social media, we have removed the original video.
"We will apply a warning screen to future uploads of the video intended to raise awareness or condemn this tragedy, and limit accessibility to people over the age of 18," the spokesperson added. "We will remove instances of videos from Facebook that are shared supporting or encouraging such acts of violence."
ABC News and KTRK contributed to this report.