The footage started circulating on social media showing the Oscar-winning actor walking along a street in Tower Hill with her husband, American film director Taylor Hackford.
The video, which was filmed last year, showed the 80-year-old smiling and greeting the man filming and asking if he was OK.
However, he can then be heard swearing at Mirren over her support for Israel.
In the footage, the man said: "And there is Helen Mirren the avowed Zionist. You said Israel should last forever because of the Holocaust. And she was very happy the Palestinians' houses were gone.
"You are an evil Zionist bitch. And you (Hackford) as well, f*** you as well."
Dame Helen's husband then stepped in and told the man to "f*** off" and leave them alone several times.
The clip was first posted by an anonymous account called Anti-Fascist Action UK.
Police said they are trying to get in contact with Mirren to see if she wants to report the incident formally.
In a statement, a Met spokesperson said: "We are aware of a video circulating online, showing a man and a woman being subjected to anti-Semitic verbal abuse in Tower Hill.
"It is believed that the incident took place at the end of last year.
"Officers are currently reviewing the footage and making attempts to contact the victims to establish whether they would like to report the incident."
Mirren, who is not Jewish, has long been a vocal advocate for Israel and last month signed an open letter alongside Boy George and Sharon Osbourne in which she pledged her support for the country's inclusion in the Eurovision Song Contest.
Throughout her career she has also played several well-known Jewish figures, including Maria Altmann in Woman In Gold and former Israeli prime minister Golda Meir in the 2023 film Golda.
While promoting Golda, she said: "I believe in Israel, in the existence of Israel, and I believe Israel has to go forward into the future, for the rest of eternity. I believe in Israel because of the Holocaust."
Mirren first visited Israel in 1967 not long after the Six-Day War, where she volunteered on Kibbutz HaOn near the Sea of Galilee.
She has previously criticised Israeli Prime Minister Benjamin Netanyahu, disliking his "male" style of leadership.
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