The injured stuntman was reported in stable condition following a five-hour operation.
Police said the two men were performing a stunt involving an explosion on an inflatable boat on the Ognyanovo dam just outside the capital city of Sofia.
The stuntmen's names and nationalities were not disclosed.
Sylvester Stallone, Bruce Willis and Arnold Schwarzenegger star in the film.
In a statement, the production company Nu Image/Millennium Films confirmed the "unfortunate accident," adding "the filmmakers are working closely with the authorities."
The Associated Press contributed to this report.