Northern Rail also said: "Due to damage to the overhead electric wires between Leeds and Wakefield Westgate the line is blocked."
Services running through these stations will be cancelled or delayed by up to 30 minutes.
A replacement Leeds to Wakefield Westgate Road replacement bus service has been requested.
Northern have confirmed that a ticket acceptance is now in place with CrossCountry services running between Leeds and Sheffield.
Customers are being advised to allow for extra time and plan ahead.
The Met Office has issued an amber 'be prepared' warning because of expected strong winds from 4pm today and into Thursday morning.
It could see 60-70mph gusts across the region.
A second storm, Eunice, is expected to arrive in the region on Friday, bringing very strong winds with 60 – 70 mph gusts are possible inland, possibly even stronger in some places.