Justin Terney, 22, died from his injuries in hospital on Monday morning after suffering three gunshot wounds during the confrontation on Sunday night.
"I'm deeply saddened to hear the news of Tecumseh Police Officer Justin Terney who passed away this morning", the statement reads.
The suspect was also shot and was in intensive care Monday morning, Kidney added. Kidney said the man ran away as Terney checked with dispatchers to see if he had any outstanding warrants.
Terney pulled over a vehicle about 11:30 p.m. Sunday in Tecumseh, 35 miles southeast of Oklahoma City, according to police. He said Terney chased the man on foot and used a stun gun, but that failed to stop the man, who then shot at Terney.
Both wounded men were taken to OU Medical Center.
Fallin said she intends to order all flags on state property to be flown at half-staff on the day of Terney's funeral, which hasn't been scheduled.
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It was at that point when Shepard is believed to have opened fire on Officer Turney, shooting him five times.
This was a devastating blow to the Tecumseh Police Department.
One hundred and thirty five officers were killed in the line of duty a year ago, according to preliminary data compiled by the National Law Enforcement Officers Memorial Fund.
Tecumseh officers are being offered counseling services, Kidney said.
The shooting suspect was also taken to the hospital, but his condition was not known.
Kidney told KFOR that several officers and community members set up a blood drive for Officer Terney. No details have been released about the suspect's identity.
"He was losing a lot of blood so we knew that we needed that", Kidney said.