Santa Fe County Sheriff's Office said deputies responded to a request to do a welfare check at the home on Wednesday afternoon and found Hackman, Arakawa and their dog dead.
The police said it was an active investigation but they did not believe that foul play was a factor.
Hollywood star Hackman, 95, and Arakawa, 63, had been married since 1991.
Hackman received two Oscars, two BAFTAs, four Golden Globes and a Screen Actors Guild Award in an acting career that spanned six decades.
He secured the best actor Oscar in 1972 for his role as Detective Jimmy "Popeye" Doyle in The French Connection.
Hackman landed a further Academy Award in the best supporting actor category for his part in 1992 western Unforgiven, directed by Clint Eastwood.
News of his death comes just four days before this year's Academy Awards ceremony.
The couple's home is in a gated community just outside New Mexico's capital city.
Hackman moved to the area in the 1980s, where he was often seen around town and served as a board member of the Georgia O'Keeffe Museum in the 1990s, according to the local paper, The New Mexican.
Aside from appearances at awards shows, he was rarely seen in the Hollywood social circuit and retired about 20 years ago.
His was the rare Hollywood retirement that actually lasted.
In his later years, he wrote novels from the hilltop ranch that provided a view of the Rocky Mountains.
Born in California in 1930, Hackman left home at age 16 to enlist in the Marine Corps and served from 1947 to 1952 as a field radio operator and then as a broadcast journalist.
He went on to study journalism and television production at the University of Illinois, but later pivoted to pursue an acting career.
Hackman had a few TV and theatre roles before breaking through with his performance in 1967's Bonnie And Clyde, which starred Warren Beatty and Faye Dunaway in the titular roles, which landed him an Oscar nomination for best supporting actor.
He also picked up Oscar nods for his role in 1970's I Never Sang For My Father and 1988's thriller Mississippi Burning.
The actor secured a new cohort of fans for his portrayal of supervillain Lex Luthor in the 1978 Superman film starring Christopher Reeve in the eponymous role and Marlon Brando as Jor-El, Superman's biological father.
He reprised the role for its subsequent sequels, 1980's Superman II and 1987's Superman IV: The Quest For Peace.
Hackman acted opposite many Hollywood heavyweights in his time including Al Pacino in 1973's Scarecrow, Gene Wilder in 1974's Young Frankenstein and Warren Beatty and Diane Keaton in 1981's Reds.
His other notable roles included the hit movies The Poseidon Adventure from 1972, 1974's The Conversation and Runaway Jury in 2003.
He took a comedic turn playing a conservative senator in 1996's The Birdcage alongside Robin Williams and Nathan Lan, who star as a gay couple.
Hackman also featured in the star-studded cast of Wes Anderson's The Royal Tenenbaums, with Welcome To Mooseport in 2004 marking his last big screen appearance.
with Reuters and AP
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