Cpl. Gale Stauffer, 38, and a second officer responded to the robbery Monday at the Gloster Creek Village branch of BancorpSouth, WTVA, Tupelo, reported.
Both were shot as multiple suspects fled the scene, Tupelo city spokeswoman Sarah Robinson said.
Stauffer died and the second officer was in critical and guarded condition at a hospital.
"This is a day that no family, no law enforcement agency or city wants to endure," Mayor Jason Shelton said.
Witnesses said the suspects fled either in a white Yukon or a smaller SUV. Police offered a $50,000 reward for information about the suspects' whereabouts.
The investigation was turned over to the FBI.