A 34-year-old woman, who is a former Ministry of Defence employee, was arrested at her Rotherham home on suspicion of misconduct in a public office.
A 31-year-old man, a serving member of the armed forces, was picked up at the same address on suspicion of aiding and abetting misconduct in a public office.
They are being held at a local police station.
The pair were arrested at 6am as part of the Metropolitan Police’s Operation Elveden, which is investigating allegations of inappropriate payments to police and public officials.
Police said that in total 52 people have been arrested as part of the operation, which is connected to the Met Police’s phone-hacking inquiry Operation Weeting.
Scotland Yard said the arrests were the result of information provided by News Corporation’s management standards committee.