Currently Britain's ambassador to the United Nations, Sir John will take up his post as MI6 head, in charge of Britain's spying operations abroad, in November.
But his wife Shelley Sawers's posting on the social networking site has breached secrecy, by exposing about where they live and work, their friends and where they go on holiday.
Edward Davey, the Liberal Democrat Foreign Affairs spokesman, called on Gordon Brown to launch an inquiry into whether the Facebook disclosures had compromised Sir John's ability to take up his MI6 post.
Shelley posted photographs of the family's holidays and gave details of the location of the family's flat in London and the whereabouts of their three children and of Sir John's parents.
On June 16, the day Sir John's MI6 appointment was announced, she posted 19 pictures of the couple on holiday with their friends in the West Country earlier that month. The lapse revealed the couple's friendship with senior diplomats and actors.