Avon and Somerset Police said that in the early hours of September 25 four men allegedly broke into a building housing items from Bristol Museum's collection on the British Empire and Commonwealth.
The burglary had not previously been publicised.
The police are appealing for help to identify the men from CCTV footage which showed them walking along a street.
"The theft of many items which carry a significant cultural value is a significant loss for the city," police officer Dan Burgan said.
Items stolen include medals, badges and pins, necklaces, bangles and rings, decorative items such as carved ivory, silver items and bronze figurines.
Natural history pieces, including geological specimens, are also believed to have been taken in the burglary.
Bristol City Council released images of an elephant carved in ivory, an ivory statue of the Buddha, a ship lantern and an Emancipation token.
The British Empire and Commonwealth Collection at Bristol Archives documents the links between the United Kingdom and countries in the British Empire from the late 19th century to recent times.
It includes the household belongings, souvenirs, photographs and papers of British people who lived and worked in the colonies.
There are about 2000 items in the film collections dating from 1920 to the 1970s, with footage from India and countries in Africa, and about 500,000 photographs dating from the 1860s to the 1970s.
with PA
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