Crews responded quickly to the fire, containing it in 20 minutes and saving the rest of the building from damage.
But the apartment was left in a bad state.
Battalion Chief Rob Pitt told the Redding Spotlight that residents of the apartment where the blaze began would have to move out.
"They are going to have to find another place to live. The unit they were living in is uninhabitable," Pitt said.
Officials said the fire caused more than US$14,000 ($19,523) worth of damage.
Wolf spiders aren't poisonous but can inflict a painful bite if feeling threatened.
They are especially common in California and more than 200 species of the arachnid live throughout the country.