A spokesperson for News of the World confirmed Weathrup's arrest but said the paper is not making any further comment at the present time.
The Metropolitan Police confirmed detectives from the Operation Weeting team arrested a 55-year-old man at 8am and took him to a London police station.
"He remains in custody for questioning after being arrested on suspicion of unlawfully intercepting mobile phone voicemail messages," the Met said in a statement.
Weatherup's arrest follows that of two News of the World journalists, chief reporter Neville Thurlbeck and former head of news Ian Edmondson, who were questioned by Scotland Yard on 5 April and later released on police bail until September.
Scotland Yard relaunched its inquiry into phone hacking at the News of the World in January after receiving "significant new information".
On Friday News International admitted liability and on Sunday the paper apologised to readers.