The Sun published the expletive-laden audio in which Cruise said: "If I see you doing it again, you're... gone."
The paper said Cruise had seen two crew members "standing too close to one another in front of a computer screen".
Variety and Reuters quoted sources confirming the audio was genuine.
Filming is currently taking place in the UK. The Sun did not say when the incident happened, but film-makers returned to the country in early December, according to Reuters.