Greig Box-Turnbull, 37, was arrested by police as part of Operation Elveden, an investigation into corrupt payments to public officials.
Box-Turnbull worked at the tabloid until March, and is currently a press officer with Westminster City Council on secondment to Richmond Council.
A prison officer and a 50-year-old woman were also arrested in south London and Kent.
A Westminster spokesman said: "We have yet to speak to the employee. With the possibility of further legal action it would clearly be inappropriate to comment further."
It is thought that the allegations are connected to his time as a journalist, reports BBC News.
Operation Elveden is being run alongside Operation Weeting, the inquiry into the hacking of voicemails.
The spokesman added: "Today's arrests relate to suspected payments to a public official and are not about seeking journalists to reveal confidential sources in relation to information that has been obtained legitimately."
A Sun reporter was among three people arrested in the probe last month.