The rail operator said that the railway line had become blocked "due to the severe weather", but did not reveal a specific reason for the delay, amid nationwide fears of railway lines buckling in the extreme heat.
Northern said customers are advised not to travel between Scarborough and Hull on Monday July 18 and that alternative transport will not be provided while the do not travel warning is in place.
Scarborough officially smashes temperature record as Met Office confirms new hottest day
RNLI issue weever fish warning for Yorkshire coast
Whitby Regatta 2022: Red Arrows unable to display over town as sea fret rolls in
IN PICTURES: Historic photographs from when the Yorkshire Coast looked very different to how it does now
Whitby Regatta 2022: 25 of the best photos as event goes ahead despite sea fret disruption
It said services running to and from these stations may be cancelled and disruption is expected to continue until 2am on Wednesday July 20.
Train services between Scarborough and Sheffield have also been cancelled, Northern said, with disruption between Scarborough and Filey, and Scarborough and York.
Northern said that passengers should only travel if essential on Monday July 18 and an amended timetable will be in place, with short-notice delays and cancellations expected.
A do not travel warning is in place for Tuesday July 19.
TransPennine Express has also warned that passengers should expect severe disruption due to the extreme weather.
Kathryn O'Brien, Customer Service and Operations Director, said: "With weather warnings in place between Sunday and Monday and a number of speed restrictions planned to be imposed on Monday and Tuesday, we will be running an amended train plan and are urging people to only travel if absolutely necessary on these dates.
"This is likely to be some of the hottest weather we've ever seen, and it's really important that anyone making an essential journey is prepared and brings water and sunscreen along with them.
"Journeys will take longer than usual, and further disruption is likely. Anyone using our services on Monday and Tuesday should check before they travel and allow plenty of extra time."
Network Rail said that railway lines in direct sunshine can be 20°C hotter than the air temperature and because rails are made from steel, they expand as they get hotter, and can start to curve – which is known as 'buckling'.
It said most of the rail network can operate when track temperatures heat up to 46°C – roughly equivalent to air temperature of around 30°C – but rails have been recorded at temperatures as high as 51°C.
Even with prevention methods in place, which include running trains at slower speeds, rails can still buckle, which requires the line to be closed and the track to be repaired before trains can run again. This often disrupts journeys as engineers have to wait until the temperature has dropped before they can carry out essential repairs.