The former Chicago police officer-turned-actor died of a blood clot in his lung, publicist Lori De Wall said in a statement.
While serving as a police consultant on the 1981 film "Thief," director Michael Mann gave Farina a small on-screen role, which led to an acting career in which Farina typically played police officers or mobsters.
He later collaborated with Mann on the 1986 TV movie "Manhunter" and the 1980s detective series "Miami Vice."
Farina's other small-screen credits included turns on the dramas "Luck" and "Crime Story," as well as in the miniseries "Empire Falls."
The actor began his two-year stint on "Law & Order" in 2004 and has also appeared in the films "Midnight Run," "Get Shorty," "Bottle Shock," "Saving Private Ryan," "Striking Distance," "Another Stakeout," "Little Big League," "Snatch," "The Mod Squad," "Big Trouble" and "Out of Sight."
Dick Wolf, creator of "Law & Order," said in a statement to EW.com Monday: "I was stunned and saddened to hear about Dennis' unexpected passing this morning. The 'Law & Order' family extends sympathy and condolences to his family. He was a great guy."