Turner, who was CIA director under President Carter, was in a San Jose hospital, authorities said Sunday.
His wife, Eli Karen, was killed in the Saturday afternoon crash, which occurred shortly after the Taxi Aereo Centroamericano flight took off from San Jose, U.S. Embassy spokesman David Gilmour said.
Also killed in the crash were Siegfried and Therese Richert of San Francisco, and Spaniard Antonio Sanchez Diaz, according to Gilmour and Javier Montero, chief of operations for Costa Rica's Judicial Investigation Organization.
Most of the passengers aboard the Czech-built LET 410 were Spaniards.
Investigators were still looking into what caused the plane to fall from the sky and plunge into a house in an upscale neighborhood near the Tobias Bolanos airport, Red Cross officials said.
Three people were in the house, including a Nicaraguan housekeeper who suffered minor injuries.
"It was like a bomb. Pieces of cement, wood and even a wall fell on top of us," the housekeeper, Yamileth Saenz, told the daily La Nacion.
In addition to Turner, the injured passengers and crew included nine Spaniards, two French citizens, one Salvadoran and three Costa Ricans, the Red Cross said. Most were in stable condition in San Jose hospitals Sunday.
The Costa Rican pilot was seriously injured, according to Pamela Villalta, spokeswoman for the San Juan de Dios Hospital.
The plane had been destined for the Tortuguero national park on Costa Rica's Atlantic coast.
It was unclear whether heavy winds at the time played a role in causing the crash.
"I was coming up the street when suddenly I saw the plane start to fishtail," one witness, Pedro Chinchilla, told the daily La Republica. "It fell, and then I heard a loud noise, like a hurricane. When I reached the site I could hear screams coming from inside the house."
By Eric Nunez