A number of people have reported seeing passengers being handed the so-called fat cards.
A Twitter user posted a picture of one of the cards, which she said she had been given on the tube, describing it as "hateful and cowardly".
British Transport Police (BTP)used Twitter to say that it was "aware of the leaflets being distributed" and urge anyone who had been handed one to contact them.
"It's really not glandular, it's your gluttony...Our organisation hates and resents fat people. We object to the enormous amount of food resources you consume while half the world starves," the cards read.
"All of our customers have the right to travel with confidence and this sad and unpleasant form of antisocial behaviour will not be tolerated," said Steve Burton, director of enforcement and on-street operations.