The poster of Obama, wearing The Joker's trademark white face make-up and elongated lips, also carries the word "socialism" above and below his image, FoxNews.com reported Tuesday.
Obama's healthcare policy, which includes a public medical insurance option, has been criticized by opponents as opening the door to a government takeover of the nation's healthcare system.
Fox News Channel said it was unclear who produced the posters.
The Joker's character in "The Dark Knight" was an anarchist, not a socialist.
Heath Ledger, who died Jan. 22, 2008, of an accidental drug overdose, won an Oscar in 2009 for his portrayal as Batman's nemesis.