Kahlo, a renowned painter, has been a Mexican icon since her death in 1954.
She created around 200 paintings over the course of her lifetime and became a symbol for the feminist movement in the 1970s.
Christopher Landau, who was sworn in as US ambassador to Mexico last month, tweeted about the painter on 1 September.
“I admire her free and bohemian spirit, and she rightly became an icon of Mexico around the whole world,” he said on Twitter, following a visit to Kahlo’s house.
The building, in Mexico City, is now a museum.
“Didn’t you know about the horrors committed in the name of that ideology?”
His tweet prompted fury from Mexicans online.
Many criticised the US or its long history of interfering in the internal affairs of Latin America and other countries around the globe, often to counter socialist governments.
“In the name of fighting that ideology, the US killed children in Vietnam by bombing entire villages and supporting dictatorships throughout Latin America,” said one Twitter user.
The Mexican Communist Party also responded to Mr Landau’s comments.
“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,” a party spokesperson said.
“Don’t show your ignorance anymore, imitating Trump.”
Kahlo and her husband, the muralist Diego Rivera, embraced Marxism and supported Josef Stalin, the Soviet dictator.
Stalin was responsible for the deaths of millions of people, many of whom died in the Gulag labour camps.
Some responses to Mr Landau were supportive, with tweeters accusing the current Mexican president, Andres Manuel Lopez Obrador, of emerging from the same Marxist school of thought.
The ambassador has to navigate a volatile bilateral relationship between the US and Mexico.
Donald Trump frequently berates Mexico over immigration and trade.
Additional reporting by agencies
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