The helicopter's two other passengers were an official from the country's organized crime investigation unit and another police officer. They were taken to a hospital and were in serious condition, the statement said.
The crash happened at about 5 p.m. in a mountainous area in the center of the state, said Veracruz public safety spokeswoman Nohemi Guzman. The helicopter had gone to a prison in Villa Aldama. The identities of the prisoners who were transported were not released and the government did not say what crimes they were charged with.
Guzman said investigators believe that strong winds and low visibility may have contributed to the accident.
Witnesses said they saw the helicopter swaying before it crashed.