Sean Bolton was hospitalized late Saturday, where he died from multiple gunshot wounds, according to the Commercial Appeal.
The suspected driver of a car Bolton had pulled over in a routine traffic stop remains at large.
"We are using all the means available to us to find the people responsible for this," the publication quoted Memphis Police Director Toney Armstrong as saying.
Mayor A.C. Whatrton was cited as saying this is the third killing of a law enforcement official in Memphis in over four years.
Chattanooga, in eastern Tennessee, was the site of a deadly attack on an armed forces recruiting center in July, which investigators classified as an act of domestic terrorism.