The box -- which city officials said is worth $800,000 -- was made between 1869 and 1878 by San Francisco goldsmith A. Andrews. It was stolen Jan. 7, the San Francisco Chronicle reported.
The museum released a picture of the box Wednesday.
Officials said the box was stolen by a thief believed to also be responsible for the theft of gold nuggets during a museum break-in Nov. 12.
The suspect was caught on video by surveillance cameras during both thefts, entering the museum through a locked door that leads to an outdoor garden at the museum.
Police said the suspect used an "unknown object" to get in.
Museum officials have offered a $12,000 reward for information leading to the return of any of the stolen items.