The Met have confirmed the officer, who is his 40s, was originally arrested on suspicion of her kidnap, and then further arrested on suspicion of murder.
He was also arrested over a separate allegation of indecent exposure.
The force said he is a member of the Parliamentary and Diplomatic Protection Command and his primary duty is uniformed patrol of diplomatic premises.
Officers continue to search locations in London and Kent, including a property in Deal and an area of woodland near Ashford.
Following the arrest of the police officer, the Metropolitan Police has made a referral to the Independent Office for Police Conduct.
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.
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.
A force spokesman said: "A man arrested in connection with the disappearance of Sarah Everard remains in custody at a London police station.
"The man, who is aged in his 40s, was arrested on the evening of Tuesday, 9 March on suspicion of kidnap. Today, Wednesday, 10 March, he has been further arrested on suspicion of murder and a separate allegation of indecent exposure.
"The man is a serving Metropolitan Police officer in the Parliamentary and Diplomatic Protection Command. His primary role was uniformed patrol duties of diplomatic premises.
"A woman, who is aged in her 30s, was also arrested on the evening of 9 March on suspicion of assisting an offender. She remains in custody.
"Officers are searching locations in London and Kent including a property in Deal and an area of woodland near Ashford.
"Following the arrest of the police officer, the Metropolitan Police has made a referral to the Independent Office for Police Conduct."