The group, made up of 60 prominent movie critics from newspapers, magazines and other media outlets nationwide, chose Daniel Day-Lewis as best actor for his acclaimed performance in the title role in "Lincoln."
Best supporting actor went to Matthew McConaughey for the male stripper film "Magic Mike," while Amy Adams won best supporting actress for "The Master."
In choosing "Amour" for its top prize, the critics were more in line with European honors such as the Cannes Film Festival which awarded it the Palme D'Or, than with earlier US awards, many of which went to presumed Oscar frontrunner "Zero Dark Thirty."
In the film, Riva plays a woman who suffers a stroke, challenging her and her husband, played by Jean-Louis Trintignant, who becomes her caretaker. Isabelle Huppert plays the couple's daughter.
The stars are among France's most revered actors, while German-born Haneke has been honored for many previous films such as "The White Ribbon" and "The Piano Teacher," with a canon that often hews more towards the bleak, brutal and disturbing than the overtly sensitive.
In other awards, the critics gave the nonfiction, or documentary prize, to "The Gatekeepers," which looks at the Israeli security agency Shin Bet, while Tony Kushner won best screenplay for "Lincoln." Best cinematography went to "The Master."
"This Is Not a Film" took the experimental film prize, while the critics gave two special film heritage honors to Laurence Kardish, senior film curator at the Museum of Modern Art, and to Milestone Film and Video for its ongoing Shirley Clarke project.
The critics' awards are among the last handed out in the run-up to the Oscar nominations, which will be announced on Thursday in Los Angeles, with the Academy Awards gala slated for February 24.
"Amour" is Austria's official submission for the best foreign language film category.