The operator has issued “do not travel” advice for journeys between Manchester and Liverpool to Edinburgh and York, Newcastle, and Edinburgh.
The warnings follow Storm Amy, which is expected to bring gale-force winds, with any trains that are able to run expected to be affected by delays and short-notice cancellations.
Andrew McClements, customer experience and transformation director at TransPennine Express, said: “Our top priority is the safety of our customers and colleagues.
“In line with other operators, we will do everything possible to keep people moving under difficult conditions, however due to the weather warnings in place on Friday afternoon and Saturday morning, we are having to issue advice not to travel on our Anglo-Scottish routes.
“We urge anyone travelling on the affected routes on Friday afternoon and Saturday morning to reconsider their plans and to follow the guidance provided.”
Passengers are advised to visit the Transpennine Express website for the latest information.
The affected routes on Friday, October 3, include Preston to Edinburgh from 12pm and Newcastle to Edinburgh from 4pm.
Passengers are also advised not to travel on the following routes on Saturday morning, October 4: Preston to Glasgow/Edinburgh and York to Newcastle/Edinburgh until 12pm.
Customers with tickets for the impacted routes can use them on Sunday, October 5, at no extra cost or request a full refund.
The disruption comes as the UK braces for the impact of Storm Amy, with amber and yellow weather warnings in place across Scotland and north-west England.