It is the first time Scotland Yard has indicated it has identified a suspected plot to intercept telephone voicemails involving the newspaper group.
The four, including ex-Sunday Mirror editor Tina Weaver and current People editor James Scott, were later bailed, the BBC reports.
The Metropolitan Police said they have been asked to return to police stations on various dates in April.
According to the report, police working on Operation Weeting said three men, aged 40, 49 and 46, and a 47-year-old woman were held in south-east and south-west London on suspicion of conspiracy to intercept telephone communications.
An email to staff from Simon Fox, the chief executive of parent company Trinity Mirror, confirms the names of four people arrested.
The email said another serving members of staff, Nick Buckley, the deputy Editor of the People and Mark Thomas, a former editor of the newspaper were also held.