Following a visit on Sunday to Kahlo's house, which has been turned into a museum after her death in 1954, Cristopher Landau sent out a tweet asking if the acclaimed artist had not been aware of atrocities committed in the name of that ideology.
"I admire her free and bohemian spirit, and she rightly became an icon of Mexico around the whole world," the US ambassador, who assumed office last month, wrote in Spanish.
"What I do not understand is her obvious passion for Marxism, Leninism, Stalinism. Didn't she know about the horrors committed in the name of that ideology?" he wrote in comments that come amid frayed relations between the two neighbours over trade and immigration.
Few Mexicans have enjoyed greater global recognition than Kahlo, who spent long periods bedridden after a traffic accident in her youth, attained international fame following her death and became a feminist symbol in the 1970s.
She created some 200 paintings, sketches and drawings - mainly self-portraits - in which she transformed her misfortune into works of bold colour.
Kahlo and her husband, muralist Diego Rivera, embraced Marxism and supported Soviet leader Joseph Stalin, after initially backing his rival, revolutionary Leon Trotsky.
Landau's tweet drew sharp reactions, with many Mexicans blasting the US for its long history of interfering in the internal affairs of Latin America and other countries around the globe, often to counter socialist governments.
"How many deaths have caused [the US] interventions? Iraq, Afghanistan, Grenada, Vietnam, Korea, Hiroshima and Nagasaki, Operation Condor ... and we don't talk about the extermination of Native Americans or the economy of slavery," A Fuertes wrote on Twitter.
"In the name of fighting that ideology, the US killed children in Vietnam by bombing entire villages and supporting dictatorships throughout Latin America," said user @Quetzalcoaltl1.
The Mexican Communist Party weighed into the debate, saying: "Ambassador Landau, Comrade Frida was consistent with humanism, the search for democracy and freedom of Mexico's workers and people, and therefore she was a Marxist-Leninist, and of course Stalin's admirer. Don't show your ignorance any more, imitating Trump."
Some of the comments however, were supportive, and accused the government of President Andres Manuel Lopez Obrador of emerging from the same Marxist tradition.
"Good afternoon ambassador," Carlos Alberto, a social media user wrote.
"It is not so worrying that Frida was unaware of the disastrous effects of Leninism and Marxism, the really worrying thing is that the current Mexican government intends to impose mechanisms inherited from [the same ideology]."
The US Embassy in Mexico said it did not have further comment about the debate.
Landau was appointed by President Donald Trump, who has frequently berated Mexico over trade and immigration.