Staff at the Royal Lancers & Nottinghamshire Yeomanry Museum noticed a number of items were missing when they arrived at work on Sunday.
A search then revealed a hole had been drilled up through an archway to allow the thieves to reach into a display cabinet.
Detectives described the raid as "audacious" and "well organised".
Among the items stolen from the museum, in Thoresby Park near Ollerton, are a distinctive parcel and gilt rosewater dish - said to be the sister piece to the Wimbledon women's singles trophy.
The Hurlingham Grand Military Polo trophy, statuettes of mounted soldiers and a cavalry trumpet were also taken.
Nottinghamshire Police believe the burglary happened between 02:40 and 03:30 GMT on Sunday.
Officers believe a small hole was drilled so a camera could be used to survey the display before a larger 25cm (10in) by 30cm (12in) hole was cut through the wooden floor and cabinet.
Museum curator Steve Cox said: "It's disgusting that they've taken history from the people who have served and fought for this country.
"The items they have taken are priceless to the museum. How do you put a value on history?
"We're upset about it, but we're fighting back and we're going to rebuild from what's gone."
Det Insp Luke Todd, of Nottinghamshire Police, said: "This was an audacious, planned, and targeted attack on what is a wonderful historic building and was clearly very well organised.
"The items that were stolen are not only high in monetary value but also high in sentimental value not only to the military, but also to the wider community in the area.
"These items are worth so much more to the museum than they are melted down in their silver form."
He urged anyone with information about the theft, or who becomes aware of attempts to sell the antiques, to contact police.
The museum, which also contains a range of firearms and other weapons, has checked its collection and accounted for all other items.
Thieves stole a haul of "priceless" silver military antiques by cutting through a museum's floor.