The plane's pilot, Jose Francisco Ortiz, 34, of Tampico, Mexico, suffered burns to 90 percent of his body in the Wednesday night crash, said Hidalgo County Justice of the Peace Rosa Trevino.
The plane's only passenger, an unidentified woman from Tampico, died in the crash. Authorities withheld her name pending notification of relatives.
It was unclear where Ortiz was being treated Thursday morning.
The plane was traveling from Houston to Tampico when it stopped to refuel Wednesday evening at McAllen-Miller International Airport, said Gabe Covarrubia, an employee of McCreery Aviation at the airport.
The single-engine Lancair IV-P made it only 2.5 miles (4 kilometers) before it crashed in an area of roads and a sorghum field, scattering debris for about 50 feet (15 meters).
More evidence appears about the arrival of Syrian jihadists that have been transferred by Turkey from the north-west of Syria to support the Islamist government led by al-Serraj