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".
Since 9/11, American Muslims, estimated between six to seven million, have become sensitized to an erosion of their civil rights, with a prevailing belief that America was targeting their faith.