The British band was scheduled to play a concert at the museum last week through a ceramic sculpture designed to explode under the force of their music.
But the museum has decided that the noise levels threatened the safety of the 150-year-old building.
“It is with regret that we have taken the decision to cancel the one-off Napalm Death performance in collaboration with our ceramic artist-in-residence Keith Harrison,” it said in a statement.
“A further safety inspection has revealed concerns that the high level of decibels generated by the concert would damage the historic fabric of the building.”
The band, whose albums include titles such as “From Enslavement to Obliteration”, were not available for comment.
Vocalist Mark “Barney” Greenway had said before the cancellation that the band liked to explore the concept of “sound as a weapon”.
“The noise element of music should never be understated,” he said.