Everard was last seen on March 3 in Clapham, south London.
The policeman remains in custody at a London police station, the police said.
“A woman was also arrested at the same location on suspicion of helping a criminal,” the statement added. “She was also arrested at a London police station.”
The arrest is “a serious and significant event,” the police said.
“We will continue to work at full speed on this investigation, but the fact that the arrested man is a Metropolitan Police officer on duty is shocking and deeply disturbing,” said assistant commissioner Nick Ephgrave.
Chief Inspector Katherine Goodwin said, “This is a significant development in our investigation. This is a rapidly moving investigation and we are doing everything we can to find Sarah.”