"Everybody is just in shock. It's small-town America," said Jacqueline Junca, the tribe's secretary and treasurer.
Police didn't immediately release the names of the officers. Authorities said they will do so at a Monday news conference.
Tribe councilman Toby Darden said the slain officer was married and had two grown children, but he declined to give his name.
"He's a real great guy. Extremely dedicated to his job. Very brave," Darden said.
He was one of seven full-time officers who patrol a 260-acre reservation that has roughly 150 homes, a grocery store, a small school and government offices.
"Everybody knows the officers personally," Darden said. "It's devastating."
Junca said the tribe has around 1,200 members, roughly half of whom live on the reservation.
Access to and from the casino was restricted for roughly 90 minutes as a precautionary measure while police responded to the shooting, said casino spokeswoman Nancy Herrington. Charenton is located about 45 miles southeast of Lafayette.
"We are very much in business and have been," Herrington said later Saturday. "We have events tonight. All of those are taking place."
A spokeswoman for the sheriff's office and a tribal police dispatcher referred questions about the shootings to the State Police.
"We've got a lot of unanswered questions," State Police Capt. Doug Cain said.
One of the injured deputies was taken to a hospital in New Orleans and the other was taken to a Lafayette hospital. Both were listed in critical but stable condition Saturday evening, Hammons said.