Network Rail is warning that the disruption could continue until 11pm tonight, with a number of services already being delayed or cancelled.
Engineering staff were expected on site by 4.15pm to carry out investigations and try to rectify the fault that had forced the closures of all lines through Mirfield.
The lines have now reopened, but delays are expected to continue for the rest of the evening.
Grand Central, Northern and TransPennine Express services are all being affected.
Passengers are being warned that trains may be cancelled, amended or delayed by up to 30 minutes.
Buses are replacing cancelled services between Huddersfield and Wakefield.
Northern passengers may use TransPennine Express between Huddersfield and Leeds.
TransPennine Express passengers may use CrossCountry between Leeds and Newcastle and East Midlands Trains between Manchester Piccadilly and Liverpool Lime Street.