Officer Verdell Smith, 46, was fatally struck downtown on Saturday night, Memphis Police Department Director Mike Rallings said.
The string of violence started with back-to-back shootings that left three people injured.
Two men were critically wounded in a shooting at Westy's restaurant at about 10 p.m., Rallings said. Minutes later, an employee at the nearby Bass Pro Shops at the Pyramid
was also shot but not critically wounded.
The suspect, 21-year-old Justine Welch, fled in a car, MPD spokeswoman Sgt. Karen Rudolph said. Police lost him on nearby Interstate 55.
But he later returned to the scene, where officers were working to clear the area. That's when Welch struck and killed Smith, police said.
Welch is charged with first-degree murder, three counts of attempted first-degree murder, evading arrest, theft of property over $10,000, vehicular homicide and reckless driving, Rudolph said.
"I am angry this morning -- angry at the senseless loss of a dedicated public servant, and angry at the absolutely unacceptable level of violence in our city," Mayor Jim Strickland said in a statement Sunday.
"We must not accept this as our norm. I most certainly will not, and I will continue to act to make our city safer."
The mayor asked every Memphis resident "to remember Officer Smith's family in prayer and reflection today and in the coming days -- and to be grateful for the dangerous, important work our men and women of MPD perform every day."
Smith is survived by his father, fiancee and three children, CNN affiliate WMC
Memphis Police Association President Mike Williams said Smith was an excellent officer and father.
"He loved his son -- always talked about him, always had him with him," Williams told WMC. "I think his son is taking it really, really hard. He (Smith) had two daughters as well."