Police didn't immediately provide any additional details. A message seeking comment was left for Hackman's publicists at Guttman Associates in Beverly Hills, Calif.
Hackman and his wife have a home in Santa Fe.
The 82-year-old actor has won two Academy Awards and been nominated for three others over a career that has spanned five decades.
Hackman took the Best Actor trophy for his portrayal of Jimmy "Popeye" Doyle in "The French Connection" in 1971, and the Best Supporting Actor award for "Unforgiven" in 1992.