The fire occurred on Sunday in a block of flats in the city of Redding in northern California.
A witness living in the flat where the fire occurred told a local newspaper that the burning spider may have spread the fire across the apartment itself.
It is not clear whether the spider survived the fire. No injuries were reported but the block was evacuated.
The local fire department chief, Gerry Gray, confirmed to the BBC that a fire had taken place in an apartment block, but that the cause of the fire was still "undetermined".
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The spider was a "huge wolf spider", according to a witness quoted by the local Redding Record Searchlight newspaper.
The fire department told the paper that the blaze appeared to have been started by a blowtorch.
Redding, where the incident occurred, is 260km north of the state capital, Sacramento.
Witnesses say that the spider spread the fire when it scurried onto a nearby mattress.
The fire on the mattress was reportedly extinguished by residents, but it had already spread to other parts of the flat.
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