Marieha Mohsin Hussain held a banner depicting the Prime Minister and the former Home Secretary as coconuts, which is a racist term used to suggest that someone has betrayed their race.
A Met Police spokesperson said: "A 36-year-old woman was interviewed under caution on Tuesday, 14 November on suspicion of a racially aggravated public order act offence in relation to a placard depicting the Prime Minister and the former Home Secretary as coconuts."
Ms Hussain, from Buckinghamshire, held the sign up at the pro-Palestinian march in London when at least 300,000 protesters called for a ceasefire in Gaza.
Police made 145 arrests and nine officers were injured during the protest which clashed with Armistice Day events at the weekend. There were clashes between far right and pro Palestine groups.
A friend told The Times: "She is not the sort of person who would ever dream of doing something bad. There is not a malicious bone in her body.
"She would never do something that was a hate crime. Marieha and her family are the most peaceful, lovely, helpful people you would ever meet. I am sure she would not know it would cause any trouble."
Police are investigating a possible racially aggravated public order offence in relation to the coconut placard.
The teacher was interviewed under caution, which means she is suspected of an offence.
Under the rules, a suspect will almost always be interviewed under caution if detectives wish to gather further evidence, elicit information revealing further lines of inquiry or give the suspect an opportunity to answer the allegations.