Gove, who was carrying a bag, a file and a drink at the time, was asked by an officer where he was going.
He pointed down the street and officers then put themselves between the MP and protesters as they helped him to make his way into a nearby building.
Amid jostling as officers attempted to keep demonstrators back from the entrance, a man appeared to shout “Arrest Michael Gove”.
One person who approached Gove asked him how he justified “illegal lockdowns”.
The Met said there have been no arrests following the incident, but that they will review footage circulating online as well as officers’ body-worn video “to see if any offences occurred”.
London Mayor Sadiq Khan condemned the treatment of Gove and thanked police for stepping in.
“This is just wrong,” Khan said. “Politicians should be able to go out without being intimidated or fearing for their safety.”