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 incident happened, but film-makers returned to the country in early December, according to Reuters.
The Mission: Impossible franchise is hugely successful at the box office, starring Cruise as Ethan Hunt.
The seventh movie had to pause filming in Italy in February due to concerns about the coronarvirus outbreak, and The Sun said the actor had "personally tried to ensure there are no more delays”.
The audio clip is shown below.