There are five more injured and four unaccounted for, he said.
"Firefighters engaged in a horrific fight for several minutes. We have the fire under control. We are in the process of trying to determine if all the employees and visitors who may have been in the building are accounted for," Fire Chief Ron Blackwell told CNN affilliate KSNW
Three of the injured are in critical condition, and one is in fair condition, an official with Via Christi Health, a local hospital, told KSNW. The hospital is expecting one more patient, the official told the station.
FAA investigators are on the scene, and the National Transportation Safety Board is aware of the incident, KSNW reported.
"There is a small aircraft that went into the FlightSafety building" near Mid-Continent Airport, according to Steve Phillips, a FlightSafety International spokesman.
The plane is a Hawker Beechcraft King Air, Phillips said.
It "crashed into the roof of our training center. I have no information on how many on board," he said. "We have the manager of the training center on site, and he's making sure everyone is OK, but I don't have an answer for that."
The building is across the street from the airport, he said.
There were about 100 people inside the building at the time, Blackwell told KWCH
The FAA said the twin-engine plane lost an engine on takeoff and crashed into a two-story building, KSNW reported. The roof on the building's eastern side has collapsed, the station reported.
Video from KSNW showed thick smoke rising from the building at 10:20 a.m. (11:20 a.m. ET).
Flights were operating normally, though some roads around the airport have been blocked off, the airport said in a tweet
"The building has sustained serious damage, including the collapse of walls and ceilings," read another airport tweet