East Midlands Railway says services are being delayed by up to an hour following the incident, which has happened close to Nottingham train station.
Network Rail engineers are on site and are working to replace the stolen cables.
A spokesman said trains running through the area in both direction cannot run between Nottingham and Mansfield.
“At present we are expecting the problem to be fixed in the next three hours. As soon as the problem is fixed our priority will be to get trains running to their advertised times again.
“We expect our advertised timetable to resume on the affected routes by 9.30am.”
The train operator says it is currently arranging replacement transport and anyone travelling between Nottingham and Hucknall can use their tickets with NET trams in both directions.
For trains that are able to take the diversion between Nottingham and Kirkby, delays of up to 20 minutes can be expected in both directions.
Anyone travelling from Bulwell, Hucknall and Newstead should use the help points, or contact 0345 7125 678 to speak to staff for further information.
A spokesman also said that anyone whose overall journey has been delayed by more than 15 minutes may be entitled to claim compensation – with full details of how to claim can be found at eastmidlandsrailway.co.uk/delay.