According to the spokesman for the newspaper, Edmondson, who is assistant editor (news), was supended on full pay before Christmas, pending an internal investigation.
A statement from NOTW this afternoon said: "A serious allegation has been made about the conduct of a member of the News of the World staff. We have followed our internal procedures and we can confirm that this person was suspended from active duties just before Christmas."
The statement continues: "The allegation is the subject of litigation and our internal investigation will take place in tandem with that. If the conclusion of the investigation or the litigation is that the allegation is proven, appropriate action will be taken.
"The News of the World has a zero tolerance approach to any wrong-doing."
The allegations were made against Edmondson in the course of a lawsuit brought against the News of the World by actor Sienna Miller.
Last month, director of public prosecutions Keir Starmer QC announced that there was no admissable evidence to bring fresh criminal charges against NOTW staff in the phone-hacking case, due to a lack of co-operation from witnesses.
Edmondson was hired by former NOTW editor Andy Coulson, now director of communications for Downing Street. Coulson has consistently denied any knowledge of phone-hacking at the newspaper.
Edmondson is the second member of staff at the NOTW to be suspended in relation to allegations of phone-hacking. Reporter Dan Evans was suspended last April in relation to a different complaint, according to a News International spokesman.