Ms Everard, a 33-year-old marketing executive, went missing after leaving a friend's house in Clapham, south London, at 9pm last Wednesday, March 3.
Metropolitan Police said a serving officer with the force was arrested at an address in Kent in connection with Ms Everard's disappearance.
The man has been taken into custody at a London police station where he remains.
Assistant Commissioner Nick Ephgrave said: "The arrest this evening is a serious and significant development.
"We will continue to work with all speed on this investigation but the fact that the arrested man is a serving Metropolitan Police officer is both shocking and deeply disturbing.
"I understand there will be significant public concern but it is essential that the investigative team are given the time and space to continue their work."
Police confirmed a woman was also arrested at the same location on suspicion of assisting an offender.
She also remains in custody at a London police station.
The force said: "The Directorate of Professional Standards is aware. Sarah's family has been kept updated of these developments."
Detective Chief Inspector Katherine Goodwin said: "This is a significant development in our inquiry. This is a fast-moving investigation and we are doing everything we can to find Sarah.
"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."
Ms Everard is thought to have walked through Clapham Common towards her house in Brixton - a journey which should have taken around 50 minutes.
She was last captured on a doorbell camera walking along the A205 Poynders Road towards Tulse Hill at around 9.30pm.
On Tuesday evening, police put up a cordon outside a block of flats near where the footage was recorded.
The search was focused on the Poynders Court housing complex on Poynders Road, and forensics officers could be seen examining the area.
Sniffer dogs were also used to search the nearby Oaklands Estate and gardens in surrounding streets, while other officers were lifting covers and searching drains along the A205.
The Met said it had received more than 120 calls from the public and had visited 750 homes in the area as part of the investigation.
Ms Everard's family, including her father Jeremy Everard, who is a Professor of Electronics at the University of York, are believed to have travelled to London in the search for her.