The 7ft (2.13m) high 1950 bronze artwork Standing Figure - known locally as Yon Figure - was taken sometime on October 10-11 from the Glenkiln Sculpture Park about eight miles west of Dumfries in Scotland.
It was in a remote location at the site on Lincluden Estate and Det Insp Colin Burnie of Dumfries CID said: "It would have required some effort to remove the sculpture from the rock it was attached to and the weight of it would have meant a vehicle would have been needed to transport it."
He added: "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.
"We feel for Sir Henry Keswick who has continued to display the sculptures outdoors for all to see, despite them previously being damaged, and to now have one stolen is sickening."
A group of three men in a Ford Transit-style van in an unusual shade of blue were previously seen looking at the bronze. They are thought to be in their 20s or 30s, of average height and build and were accompanied by a collie-type dog.
The Glenkiln park was established by local landowner Sir William Keswick from 1951-76. The works on display also include: Saint John the Baptist (1878) by Auguste Rodin;Visitation(1926) by Jacob Epstein; King and Queen (1952-53), Upright Motive No. 1: Glenkiln Cross (1955-56) and Two Piece Reclining Figure No.1 (1959) by Moore.
The BBC reported that Moore said of Keswick's project: "I don't know whether he got the idea to put sculpture on his sheep farm after he saw the Battersea Park open-air exhibition, or whether he was inspired by his experiences in China, where he had lived for many years, and where, he said, there are many examples of monumental sculptures in the open air.
"In any case, he bought this piece to put on his farm in Scotland. He placed the sculpture himself on an existing outcrop of rock.
"Later I went up there and was thrilled with the beautiful landscape and at how well he had sited 'Yon Figure'."
Spate of thefts
In November last year two men were sentenced to a year in jail after admitting the theft of a sundial sculpture and bronze plinth - Working Model for Sundial 1965 - from the Henry Moore Foundation in Much Hadham, Hertforshire, which were recovered by police after an appeal on BBC's Crimewatch.
Regarding the latest theft, Richard Calvocoressi, director of the foundation, said: "We profoundly sympathise with the owners of this important sculpture, which was purchased directly from Moore by Sir William Keswick and sited on his estate, a spectacular setting which pleased Moore immensely."
Moore's Reclining Figure, worth £3m, was taken from the foundation in December 2005.
Police believe the three-tonne sculpture was melted down and sold for scrap, making perhaps just £1500.
His £45,000 painting Three Reclining Figures On Pedestals was one of three artworks stolen from a gallery in Broadway, Worcestershire, in 2010.
Contact Police Scotland through 101, or if you prefer, anonymously, through Crimestoppers on 0800 555 111.
• In a separate development, a Barbara Hepworth sculpture stolen from Dulwich Park in South London will now be replaced by a series of works by Conrad Shawcross, who won a competition to earn the honour. His Three Perpetual Chords is weighted with concrete to deter potential thieves.
Hepworth's Two Forms (Divided Circle) from 1969 was cut from its plinth in December 2011 and is believed to have been melted down and sold for scrap. It had been in the park since 1970.
The sculpture was one of an edition of six casts, one of which remains on view at the Tate-run Barbara Hepworth Museum in St Ives, Cornwall.