The heritage railway has already suspended steam services on previous occasions this summer due to the cinders from passing locomotives starting fires in vegetation beside the tracks.
As a precautionary measure, all trains today have been cancelled and Tuesday's services will be operated by diesel engines.
The North York Moors National Park has issued extreme weather warnings about the risk of wildfires due to the dry conditions.
The NYMR said in a statement: "Due to the unprecedented dry spell the UK is currently facing the North Yorkshire Moors Railway has made the difficult decision to cancel today's remaining services."
“Despite implementing changes to our services on July 8 and reducing our Moors Explorer service, we have had to cancel the remainder of today’s services. Even with reducing our steam usage and increased lineside patrols, we are still experiencing a high level of lineside fires.
"We sincerely apologise to our passengers that have been impacted by today's delays/cancellations and we have reviewed our services tomorrow to add further mitigations. Tomorrow's services will operate as planned, with services being hauled by our heritage diesel locomotives.
"Like most registered charities, we have had to navigate through the Covid-19 pandemic and we are now facing environmental challenges with rising temperatures and increased fuel/coal prices and restrictions. As the busiest heritage railway in the UK, we encourage the public to support the sector by either donating or travelling along the historic line to ensure all communities can enjoy the golden age of steam."