The force said a graphic was shared via social media on Friday and was reported by a number of officers “who were concerned by its content”.
In a statement, the Met said: “Given the context of the officer’s duties at the time, a voluntary referral has been made to the Independent Office for Police Conduct in relation to this matter.
“The Pc had been deployed as a cordon officer supporting the search operation in Kent in relation to the murder of Sarah Everard.
“The officer has been removed from these duties and placed in a non-public facing role while inquiries continue.
“The graphic does not contain photographic images, no images of Sarah, nor any other material obtained from or related to the investigation into Sarah’s murder.”
Assistant Commissioner Nick Ephgrave said: “The MPS expects its officers to behave professionally at all times and this includes how they use social media. I take allegations that any officer or officers have failed to observe these standards very seriously and have referred this matter to the IOPC.”
The force added Sarah Everard’s family have been made aware of the incident.
Serving Metropolitan Police officer Wayne Couzens, 48, has been charged with kidnapping and killing the marketing executive, who went missing while walking home from a friend’s flat in south London on March 3.