The painting is by artist John Currin and is titled "Bea Arthur Naked." It sold at Christie's auction of postwar and contemporary art on Wednesday. It had been expected to bring in between $1.8 million and $2.5 million.
Christie's hasn't said who bought it.
The 1991 oil painting depicts the late television actress nude from the waist up. Christie's said Thursday the image was based on a photograph of her with her clothes on.
Arthur gained fame for her Emmy Award-winning roles in "Maude" and "The Golden Girls" in the 1970s and '80s. She died of cancer in 2009 at age 86.