The 34-year-old woman, who previously worked for the MoD, and a 31-year-old man who is a serving member of the Armed Forces, were arrested in a dawn raid at their home in Rotherham, South Yorkshire.
The woman was detained on suspicion of misconduct in a public office and corruption, while the man was being questioned on suspicion of aiding and abetting misconduct in a public office and money laundering.
The pair were arrested as part of Operation Elveden, the Metropolitan Police's investigation into the corrupt payments by journalists. Both being questioned at a South Yorkshire police station.
A Metropolitan Police spokesman said their arrests were the result of information provided to police by the management and standards committee at newspaper publisher News Corporation.
The spokesman said: "It relates to suspected payments to public officials and is not about seeking journalists to reveal confidential sources in relation to information that has been obtained legitimately."