Authorities said the explosion occurred at the rig about 2 miles west of Coalgate in a remote area of rural Coal County about 100 miles southeast of Oklahoma City.
Matt Skinner, a spokesman for the Oklahoma Corporation Commission that regulates the oil and gas industry, said no evacuations were required in the area and there were no reports that the explosion and fire caused environmental damage that would require subsequent cleanup.
Skinner said he didn't know if the fire was still burning. Coal County Sheriff Bryan Jump, who is at the scene, was not immediately available for comment.
The state Medical Examiner's Office identified the dead as Gary Keenen, 26, of Ada, and Kelsey Bellah, 27, of Tulsa.
Skinner said two workers were critically injured at the rig, which is owned by Pablo Energy of Amarillo, Texas. He provided no names.
A telephone call to Pablo Energy was not immediately returned.
The U.S. Occupational Safety and Health Administration will investigate the cause of the explosion, Skinner said.