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.
The 33-year-old marketing executive, Sarah Everard, vanished while walking home from a friend's flat in south London on Wednesday March 3.
She was last captured by a doorbell camera walking along the A205 Poynders Road towards Tulse Hill at around 9.30pm on that day.
Late on Tuesday, the Met Police said a serving officer from the force had been arrested as part of the investigation, but in an unusual step would not reveal what he had been detained for at that stage.
On Wednesday it was announced that the officer had been arrested on suspicion of murder following the disappearance of the young woman.
Officers continue to search locations in London and Kent, including a property in Deal and an area of woodland near Ashford.
A tent was erected at the front of a house in Freemens Way in Deal, and multiple cars were taken away by investigators. Later a metal fence was put up surrounding the front garden and driveway.
A neighbour in the road said a police officer lives at the address with his "chatty" wife and two children.She said: "They just seemed like a normal, regular family, there was nothing strange about them at all."
She added that police were digging up the garden.
Matt Mullan, 29, who also lives nearby, told the PA news agency: "Last night there were police cars outside all night.
"I thought this is a bit strange, not normal for round here.
"It was about 8-9pm there was heavy traffic out there and there have been police cars outside all morning.
"It's very surprising, definitely not what you expect to see."
Another said: "You don't expect it to be on your doorstep, really.
"You see this sort of thing every day on the TV and the news but you don't expect it."
Following the arrest of the police officer, the Metropolitan Police has made a referral to the Independent Office for Police Conduct.