The crash happened at about 11pm, when a vehicle, thought to be a Seat Leon, came off the A64 near the traffic lights at the bottom of Staxton Hill.
It is unclear whether anyone was injured.
BT Open Reach engineers are currently on site but the company says giving a timescale at this stage is 'difficult' as reinstating the cabinet is a major undertaking.
A spokeswoman for BT Open Reach said: "We have engineers on site but they are currently making sure the general area is safe and waiting for the power company to send an engineer to check that it is safe in terms of power supply.
"As soon as that has been done our engineers can start checking the impact and identifying a solution to restore service.
"In the meantime I would recommend that anyone impacted contacts their service provider to log a fault. Service providers may also be able to advise on alternative methods of connections for those who need it urgently.
"In the current situation we completely understand that connectivity has never been more important and our engineers will do everything possible to get service back up and running as quickly as possible."