Authorities had yet to identify the man, but were holding a press conference Wednesday.
Davis spokesman Anthony Spangler said two staffers were inside the office at about 4 p.m. Tuesday when they smelled a strange odor and a fire alarm went off. He said one person opened the door to find burning bottles and flames up to her waist.
Staff members used a fire extinguisher to put out the flames. No one was injured.
Davis was not in the office at the time. She later spoke to reporters and called the incident, "alarming and very scary."
Davis joined the Senate in 2009.
