Ms Sarah Everard, 33, was last seen in Clapham at around 9.30pm on 3 March.
The Met Police officer was detained at an address in Kent on Tuesday evening and remains in custody at a London police station, .
A woman was also arrested on suspicion of assisting an offender.
The assistant commissioner Nick Ephgrave said “The fact that the arrested man is a serving Metropolitan Police officer is both shocking and deeply disturbing,” .
“I recognise the significant concern this will cause. It’s really important the investigative team are given the space and time to find Sarah, and they’re working at all speed to do so.”
“Every piece of information is important to us. Anything who thinks they know anything about Sarah’s disappearance should come forward.
“As a father myself of four young women, I can only imagine the anguish that Sarah’s family are feeling at this very, very difficult time.”
Ms Everard disappeared after leaving the home of a friend in Clapham at around 9pm last Wednesday, with footage from a doorbell camera showing the marketing executive walking towards the Tulse Hill area around half an hour later.
William Roache (Analysis Editor Newspresslive )