The TBI said that the man rammed his vehicle several times into police cars before getting out with a weapon.
"The officers fired striking and killing the individual," the release said, adding that no officers were injured in the immediate incident.
Officials with the Memphis Police Department reported on Twitter that after the shooting, some police officers "received minor injuries" from people throwing "bricks/rocks" at them.
The Memphis Appeal newspaper reported that a "tense standoff" escalated with dozens of people.
There were no initial reports on other arrests or the extent injuries.
Mayor Strickland posted, "Let me be clear—the aggression shown towards our officers and deputies tonight was unwarranted."