The Standing Figure was taken from Glenkiln Sculpture Park in Lincluden Estate, Dumfries and Galloway between 3pm on Thursday and 3pm on Friday.
The 1950 statue is around 7ft tall and was attached to a large rock plinth.
Officers believe the thieves used a vehicle to transport the artwork from the park, located on a moor by Glenkiln Reservoir in Shawhead, and have appealed for anyone who saw anything suspicious to contact them.
Detective Inspector Colin Burnie, from Dumfries CID, described the theft as "sickening" and said he felt for landowner Sir Henry Keswick who has continued to display the sculptures outdoors despite them previously being damaged.
"The sculpture is one of six on public display and as well as the monetary worth, it has great emotional and sentimental value to the family," he said.
"In this early stage of the investigation we have not discounted any line of inquiry. We are open minded with regards to the motive, the thieves could have targeted it for the value of the artwork or purely for its scrap metal value.
"It would have required some effort to remove the sculpture from the rock it was attached to and the weight of it would've meant a vehicle would have been needed to transport it.
"We would ask anyone who witnessed any suspicious vehicles in the area recently, including vans and larger vehicles, to get in touch. Often thieves will scope out a potential target by visiting it several times in the lead up to the incident."
The statue is one of four Moore pieces in the park, including his world renowned King and Queen sculpture, and other works by Auguste Rodin and Jacob Epstein.
Standing Figure is among a string of works by the abstract artist, who died in 1986 aged 88, to be targeted by thieves in recent years.
Two men were jailed for a year in 2012 for stealing a sculpture called Sundial and the bronze plinth of another work from the grounds of the Henry Moore Foundation in Much Hadham, Hertfordshire.
Moore's £45,000 painting Three Reclining Figures On Pedestals was one of three works of art worth a combined £230,000 stolen from a gallery in Broadway, Worcestershire in 2010.
The Henry Moore Foundation also had to carry out a security review following the theft of a two-ton piece called Reclining Figure in December 2005.
The foundation was established by the artist in 1977 to encourage public appreciation of the visual arts.
Anyone with information about the theft of the Standing Figure is asked to call Police Scotland on 101.