The artwork, which recently fetched a record-breaking $179.4 million at auction, was painted in 1955 and continues to be one of Picasso's defining pieces.
But Fox News felt it necessary to censor the cubist's classic work, leading New York Magazine's art critic Jerry Saltz to tweet: "How sexually sick are conservatives & Fox News? They blurred parts of the Picasso painting. #SickMinds."
Artist and author Gonzalo W Benard said the censorship was "pathetic”, while art writer Aruna D’Souza said: "Glad Fox News is protecting its audience from Picasso’s smutty mind."
The painting's auctioneers said the painting was "a milestone in Picasso's oeuvre and one of his most famous masterpieces".