Sarah Everard, 33, was last seen in Clapham, in the south-west area of the capital, at around 9.30pm on 3 March.
A male Met Police officer was detained at an address in Kent on Tuesday evening and remains in custody at a London police station, said Scotland Yard.
A woman was also arrested at the same Kent address on suspicion of assisting an offender, and also remains in custody.
“The fact that the arrested man is a serving Metropolitan Police officer is both shocking and deeply disturbing,” said assistant commissioner Nick Ephgrave, speaking outside Scotland Yard on Wednesday morning.
“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.”
Mr Ephgrave said police inquiries suggested that the officer arrested in connection with her disappearance “was not on duty at the time of Sarah’s disappearance”.
Describing the investigation as “fast paced”, the assistant commissioner appealed to the public to share information. “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.”
Read more: Sarah Everard: Timeline of disappearance
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.
Her family have described the 33-year-old’s disappearance as “totally out of character”. Friends and relatives have issued appeals on social media to help find her.
On Tuesday officers set up a cordon around the Poynders Court housing complex on the A205 Poynders Road, with forensics officers seen examining the area.
Detective chief inspector Katherine Goodwin said: “We have seen an overwhelming response from the public and I repeat my request for anyone with information that may be relevant to come forward, no matter how insignificant it may seem.”
The force said it would not be commenting further on the arrests at this stage.
Ms Everard’s family have been made aware of the developments in the case, as have the Met’s Directorate of Professional Standards.
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