Services have been bought to standstill throughout the region after it hit the Integrated Electronic Control Centre at York.
Some passengers have been stuck on trains in the sweltering heat after the system was hit around 10am.
Services are being affected between Leeds and York, as well as those travelling via Doncaster.
All services between York and Sheffield are affected.
Passengers are being advised to check before travelling. Some services are being cancelled.
Powergrid is preparing for potential power cuts and disruptionRachel Lowe, senior communications manager for Network Rail, said: "We know we had a lightening strike close to or on the signal box which controls all the train movements through Leeds station onto the East, West and North West.
"Basically Leeds is not in a good way - similarly the lightening has caused problems elsewhere, so we can't get south out of York, and can't get between Leeds and York."
Ms Lowe said she was buying a coffee at the station when she heard an "absolutely terrifying" bang.
She added: "It is going to be a very difficult day."
Three houses struck by lightening in YorkShe said their first priority was to get passengers on trains stranded on the lines back into the stations as soon as possible.
"It is too hot to leave passengers on the trains for too long," she added.