The Royal Armouries is set to axe jobs after a cut in government funding.
The Leeds museum, which also runs the White Tower at the Tower of London and Fort Nelson in Hampshire, said it was facing a 15% cut in grants.
A Royal Armouries spokesman said it would now have to make "substantial savings" over the next four years.
He said the museum was proposing to reorganise its staffing structure and was in talks with "potentially affected staff" and their union representatives.
The Royal Armouries employs 193 people across its three sites, 152 of them in Leeds.
But the museum's directors said they could not give details of how many jobs might be affected or exactly how much money it needed to save.
Jonathon Riley, director general and master of the Royal Armouries, said: "These are difficult times for everyone but the museum has survived in some form or other over the past 900 years and we will continue to protect and display this incredible collection.
"Ironically, this year we are seeing the highest visitor numbers since we opened our head office in Leeds and we intend to build on the public's love of the collection and the staff who present it."
The Department for Culture, Media and Sport (DCMS) announced the 15% funding cut as part of the government's spending review which saw its core budget cut from £1.9bn to £1.1bn over the next four years.