The line between York and Scarborough was blocked due to track concerns.
Engineers have been carrying out a safety inspection along the line this morning (Friday, 14 August).
Rail operator TransPennine Express said the disruption was due to last until 11.30am.
The company said it affected “Scarborough to York in that direction only”.
It added: “You should continue to travel as planned; however, your journey may be delayed.
“We are working on alternative routes to keep you moving and we will update with further information.
“You can also travel towards your destination via reasonable route.
“Passengers can use their ticket at no extra cost on a Northern service to Hull, and change for services towards Leeds with TransPennine Express or Northern.”
At 12.22pm, it issued this update: “Trains are now running at reduced speed between Scarborough and York.”
Concerns about the impact of the heatwave on railway tracks have been expressed after the derailment of a train in East Sussex yesterday.
Pictures of a section of damaged track have led people to ask whether this caused the crash or was caused by it.
Today John Whitehurst, chief executive of Greater Thameslink Railway, was asked if the railway was safe in hot weather.
He told BBC Radio 4’s Today Programme: “The railway is safe. These types of incidents are incredibly rare.
“We have control processes in place that involve inspection, temporary speed restrictions or even suspending services if that’s required.”