The blaze at 101 N.W. Front St., at the intersection with North Street, was reported about 7:30 p.m. Saturday.
Flames were engulfing the historic three-story dwelling when Carlisle Fire Company crews arrived, said Michael G. Chionchio, assistant state fire marshal.
Deputy fire marshals determined the fire started on the exterior when the vehicle struck propane gas lines feeding the building, Chionchio said, and the flames spread.
Damage was estimated at $50,000.
No one was inside the building when the fire started, Chionchio said, and there were no injuries reported.
According to the B&B’s website, The Towers was built in 1783 but dramatically remodeled in 1891 in the lavish “steamboat Gothic” style. In the early 19th century it was home to Delaware poet John Lofland, and later was owned by William Burton, Delaware’s governor during the Civil War.