Everard was last seen on March 3 in Clapham, South London.
The police officer is still detained at a London police station, police said.
“A woman has also been arrested at the same location on suspicion of assisting an offender,” the statement added. “She has also been taken into custody at a London police station.”
The arrest is “a serious and important development,” police said.
“We will continue to work on this investigation as a matter of urgency, but the fact that the arrested man is a serving Metropolitan Police officer is both shocking and deeply troubling,” said Assistant Commissioner Nick Ephgrave.
Detective Chief Superintendent Katherine Goodwin said, “This is an important development in our investigation. This is a fast moving investigation and we are committed to finding Sarah.”