National Express services will be suspended from 11.59pm on Sunday, until March.
The firm has decided to suspend the services due to tighter restrictions and falling passenger numbers.
All journeys before Monday 11 January will be completed to ensure any passengers making essential journeys are not stranded.
All customers whose travel has been cancelled will be contacted and offered a free amendment or full refund.
Chris Hardy, managing director, said: “As the vaccination programme is rolled out and Government guidance changes, we will regularly review when we can restart services.
“We plan to be back on the road as soon as the time is right and have put a provisional restart date of Monday 1 March in place – subject to change.”