"The cause is undetermined," said the actress's spokesperson. No further details were provided, but according to TMZ, who first posted news of the blaze, law enforcement says that an unattended candle started the fire on the couch.
A source tells PEOPLE that the Twilight star's two fox terriers were in the apartment at the time. Rescuers were able to save one.
TMZ.com also reports that 10 fire trucks arrived on the scene of the seven-story building after the fire began while Greene was asleep. Greene's dog reportedly died under the bed.