The gunman, identified by the Independent as 46-year-old Craig Stephen Hicks, reportedly turned himself into police.
The Chapel Hill Police Department said in a statement it was questioning a person of interest in the crime "and has reason to believe that there is no ongoing threat to the public".
Police officers reportedly responded to report of gunshots in the area around Summerwalk Circle at 5pm to find the three young Muslims pronounced dead at the scene with shots in the head.
Barakat is an American football and basketball fan. He is believed to be a dental student at the University of North Carolina and volunteered with a charity providing emergency dental care to children in Palestine.
He regularly posted on Twitter, and wrote in January: “It's so freaking sad to hear people saying we should ‘kill Jews’ or ‘kill Palestinians’. As if that's going to solve anything.”
The youngest victim, Razan, had started a degree at North Carolina State University last summer, studying Architecture and Environmental Design, and her Twitter biography read: “I like buildings and other stuff.”
The three victims were recently pictured together at the graduation of his sister-in-law, Razan, who ran a blog showing her interest in photography and art.