Fewer trains will also be running between Blackpool North and Preston, with limited rail replacement buses running in both directions.
Other services affected include Manchester Piccadilly to Manchester Airport in both directions, with fewer trains able to run and limited rail replacement buses running.
A Network Rail spokesperson said the first trains expected to be able to call at all stations would be the 17:51 GMT Blackpool North to Manchester Airport and the 18:45 Manchester Airport to Blackpool North service.
Passengers are also being advised that Northern tickets can be used at no additional cost on the Avanti West Coast service between Warrington Bank Quay and Oxenholme Lake District and the TransPennine Express service between Manchester stations and Preston.
Network Rail said it is working with the police to find the thieves.
The line closure comes as Northern services across the North West are expected to be significantly affected by train crew shortages.
Network Rail has been electrifying the line between Wigan and Bolton since 2022.
The stolen cable provided power to the overhead line equipment, which then powered electric trains across the tracks.
“I am very sorry to passengers who will be impacted by the rail closure,” Christian Irwin, Network Rail’s capital delivery director, said.
“We are working closely with the British Transport Police to provide additional security measures and to find and prosecute those accountable.”