The footage, which was shared on social media, showed the officer speaking with a demonstrator who was protesting in solidarity with the people of Palestine.
In the video, the officer can be seen chatting with a protestor and hugging her before saying “Free, Free Palestine” as other protesters reacted in celebration.
The clip was widely condemned by some who called for officers to remain impartial while patrolling the streets.
One commentator wrote: “This is a disgrace, police have to be impartial or do we now have a political wing of policing?”
Another said: “As much as the officer has her opinion and they all do - she should have reserved it and maintained her authority as a police officer! ”
Meanwhile, others were in support of the officer.
“Sounds like she has empathy for people being massacred,” one tweeted. “I have no problem with that.”
Of the footage, The Met said: “We police hundreds of events and protests every year and officers must remain independent and impartial in carrying out their duties.
“We are aware of footage circulating from the weekend.
“We’re reviewing it and a further update will be released shortly.”
In a statement to the Standard, a Met spokesperson added: “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.”
Thousands of people marched through the capital on Saturday to the gates of the Israeli embassy in Kensington, while protests took place in other cities across the UK and Ireland.
Demonstrators chanted “free, free Palestine”, and held banners calling for an end to the bombing of the territory by Israeli forces.
Former Labour leader Jeremy Corbyn appeared alongside the Palestinian ambassador Husam Zumlot to the UK at the rally.
Mr Zumlot said: “This time is different. This time we will not be denied anymore. We are united. We have had enough of oppression.
“Today we are saying enough, enough with the complicity. Thank you for standing with us.”
It comes as more than 52,000 Palestinians have been displaced by Israeli airstrikes that have destroyed or badly damaged nearly 450 buildings in the Gaza Strip, the U.N. aid agency said on Tuesday.
About 47,000 of the displaced people have sought shelter in 58 U.N.-run schools in Gaza, Jens Laerke, spokesman of the United Nations Office for the Coordination of Humanitarian Affairs (OCHA), told reporters.
Laerke said 132 buildings had been destroyed and 316 had been severely damaged, including six hospitals and nine primary healthcare centres.