Everard was last seen on March 3 in Clapham, south London.
The police officer remains in custody at a London police station, according to police.
“A woman has also been arrested at the same place on suspicion of helping an offender,” the statement added. “She has also been detained at a London police station.”
The arrest is “an important and important fact,” police said.
“We will continue to work swiftly on this investigation, but the fact that the arrested man is a Metropolitan Police officer on duty is both shocking and deeply disturbing,” said Deputy Commissioner Nick Ephgrave.
Detective Chief Inspector Katherine Goodwin said, “This is a significant development in our investigation. It’s a fast-moving investigation and we’re doing everything we can to find Sarah.”