"I am devastated, just devastated", she was quoted as saying.
No one was hurt in the blaze which occurred while Johnson and her husband were at work. "We have just the clothes on our backs".
Al.com reported that Johnson's home in Gadsden, Alabama, burned down Tuesday morning.
Local news reports no one was in the home during the fire.
Johnson told AL.com in November that during a visit to Moore's office in 1991, when she was 28, he made several inappropriate comments and then groped her as she was leaving.
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The Etowah County Sheriff's Office revealed that the fire was being reviewed by its arson task force, but, while a suspect was being spoken to, no charges had been filed yet.
"More details will be released when warrants are obtained".
Another female neighbor told Johnson that the young man in question approached her as she was leaving her home that morning and asked if she thought the house was going to burn down.
Multiple neighbors witnessed a young man known for public intoxication walking around the house during the time of the fire.
"He's been trouble in the neighborhood for a while", said Tallant, who lives across the street from Johnson and her family.
He lost the special election to Democrat Doug Jones on December 12, turning Alabama blue from red for the first time in 25 years. Leigh Corfman, who claimed Moore molested her when she was 14, alleged Moore and his campaign defamed her and made false statements as they denied her accusations.