Avon and Somerset Police arrested a 28-year-old man early yesterday morning on suspicion of the theft of lead from the roof of the Museum of Costume in the Assembly Rooms.
Security staff alerted police about two men acting suspiciously at around 4am.
The man was detained nearby and a quantity of lead was recovered.
He is in custody and has now been questioned.
Investigations are continuing to try to find the other suspect.
Any witnesses or anyone with any information is asked to call 101 quoting reference number 16970/15.