The uniformed female officer was filmed at a pro-Palestinian demonstration in London, accepting a white rose and hugging a protester.
She was heard shouting “free, free Palestine” to cheers from the crowd.
A spokesperson for the Metropolitan Police said: “We are aware of a video that has been posted on social media which shows an officer joining in with chanting while on duty at a demonstration.
“While officers are encouraged to positively engage with those attending demonstrations, they know they are not to actively participate or adopt political positions. This is vital to ensuring the public have confidence in our officers.
“The Directorate of Professional Standards has been informed and are investigating the full circumstances of this incident and to determine what further action is appropriate.”
The footage has been widely shared on social media sites, where critics called for a swift investigation.
Susan Hall, leader of the Greater London Authority Conservative Group, wrote: “The police are supposed to be neutral – this is not good enough @metpoliceuk – please investigate.”
Ms Hall shared footage from a Twitter account with a biography reading: “Conservative and Trump lover. Left wing policies have killed Europe. Anti-EU. Despise the Labour Party and Communism. MAGA 2024.”
It came after numerous protests over the Israel-Gaza conflict in London and other British cities.
Four men were arrested after antisemitic abuse was shouted from a car in Finchley on Saturday.
Footage on social media showed a convoy of cars covered with Palestinian flags passing down Finchley Road, with passengers being heard to use violent and offensive language and issuing threats against Jews.
The incident received cross-party criticism, with Boris Johnson condemning the acts as “shameful racism” that have “no place” in society.
Thousands of people marched through London on Saturday to the gates of the Israeli embassy, while protests took place in other cities across the UK and Ireland.
Since last Monday, the Palestinian militant group Hamas has fired hundreds of rockets into Israel, whose military responded by barraging the Gaza Strip with tank fire and air strikes.
The UK’s permanent representative to the UN, Barbara Woodward, has said the UK “remains committed to the two-state solution as the best way to permanently end the occupation and bring peace and stability to the region”.
“We urge all sides to show maximum restraint and refrain from taking actions which endanger civilians and make peace more difficult,” she said on Saturday.
“The United Kingdom will continue to do all it can to bring an end to this violence and work towards a more peaceful future for Israelis and Palestinians alike.”