Diversions will be in place for at least a week around Higherford while Lancashire County Council experts try to determine what caused the failure.
Ray Bennett, principal engineer, said: “We had to put safety first and close the road as quickly as possible because part of the surface had collapsed.
“We have to find out what has caused the collapse and what type of repairs are needed.
“The current closure is in place for a week, but we may have to extend this depending on how complex the repair work is.
“Diversions are in place and these should help ensure that disruption is kept to a minimum. We’re sorry for the inconvenience but hope that people’s journeys won’t be too badly affected.”