A local newspaper in Asheville reported one road washed away and work crews were trying to build a temporary bridge so residents could leave their homes.
Flooding also was reported by the weather service in Caldwell and Jackson counties.
To the east, the Rocky Mount-Wilson Airport recorded seven-tenths of an inch of rain in about 30 minutes.
The events come three days after the state emerged from drought conditions.
Forecasters are calling for the rain to taper off in the mountains and the rest of the state by Monday afternoon.