Veteran actor-director Clint Eastwood's film, which was released on December 25 and has garnered six Oscar nominations, tells the story of Chris Kyle's four tours in Iraq as a sniper.
Kyle, played by Bradley Cooper in the movie, is officially credited with killing 160 people in Iraq.
"This 'Sniper' film which has made so much noise... encourages a young person, for example a Christian or non-Muslim, to harass a Muslim as much as possible," the official IRNA news agency quoted Khamenei as saying.
Khamenei's comments, published on the website khamenei.Ir which showcases his speeches, were made three weeks ago after the early January attacks by jihadists in Paris against satirical magazine Charlie Hebdo and a Jewish supermarket that killed 17 people.
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Khamenei denounced "propaganda against Muslims in Europe and America", saying there was "no trace of aggression against non-Muslims by Muslims" since the advent of the Islamic republic in 1979.
Iran recognises three minority religions within the country -- Christianity, Judaism and Zoroastrianism -- and their adherents have certain rights.
Kyle and his friend Chad Littlefield were murdered at a Texas shooting range in February 2013. A former US Marine is currently on trial charged with both killings.