The River Skell has overflowed through the Studley Royal estate, where the abbey ruins stand, and flooded the water gardens laid out by the Aislabie family in the 18th century.
It is the worst flooding at the site since 2017.
Staff are currently assessing the extent of the damage to the historic parkland.
The National Trust's Jenni Shepherd said: "The team here are understandably heartbroken as we can only watch the flooding take hold and wait for the water to recede before we can assess next steps.
"It’s recovered before though and at the end of the day, it’s not someone’s home which we’re always mindful of.
"The abbey ruins are thankfully safe for now but we’ll be keeping our fingers crossed as this next storm rages as the Skell was certainly lapping at the West Green yesterday morning. It’s not as bad as the flooding we had in 2017 but certainly the worst we’ve seen since then."