The track is blocked in both directions with no current estimate as to when services will run again.
A spokesman for Northern said: "The mud has completely covered the track in both directions meaning we cannot run trains between Lancaster and Skipton.
"The mudslide was discovered at around 7.45am when a Lancaster to Leeds service encountered problems on the line."
The spokesman added: "We are working with Network Rail to get the track cleared as soon as possible but, given the amount of mud and debris on the line, this could take some time. We apologise to any customers whose journeys are disrupted and ask anyone planning to travel on this route to seek alternative arrangements."
Northern is in the process of trying to arrange rail replacement road transport to help keep customers on the move.