The artefact's - mostly made of silver, glass and ceramic - date as far back as the 17th century and include a lacquered gold elephant tusk vase from Japan.
The thieves gained entry to the building in Bohemia Road between 5pm on Wednesday and 8am the following morning.
The museum was closed yesterday while police collected evidence and doors were expected to open to the public within a couple of days.
Security has been stepped at the premises since the break-in and CCTV tapes are being reviewed by police.
Borough council spokesman Kevin Boorman said: "A lot of care was taken to choose items of value and we think they will be sold on. If any antique dealers are offered anything they suspect is stolen, they should contact police.
"It's very sad that visitors to the town's museum will not be able to see these items which are of international repute and part of Hastings' heritage."