It had been hoped that the 2021 event would be a mix of live music and online events.
But organisers said the continuing worldwide Covid pandemic means that will not now happen.
Customers who retained tickets from the cancelled 2020 event and Llanfest ticket holders are being contacted.
A spokesman said: "We suspended the traditional live competition strands for Llangollen 2021, and are reimagining our event in a way that can be delivered safely but which will still capture the magic of our international Eisteddfod in a digital format.
"We were hoping to create a hybrid weekend as part of this year’s offer, featuring artists from the 2020 line-up including our iconic Llanfest evening, but due to continued restrictions this cannot be realised this summer. Llanfest ticket holders will be contacted by your ticket provider for a full refund in the next week.
"We know that it will be a disappointment to many that we are not able to put on our usual Eisteddfod this year. But we remain committed to our Eisteddfod’s founding mission of bringing people together through music and dance, which will be at the heart of our alternative approach to Llangollen 2021. "
Until the pandemic struck, the Eisteddfod attracted hundreds of competitions from across the world and thousands of visitors to the July event in Llangollen.
In recent years top names in the world of music of all genres have starred in evening concerts at the Royal International Pavilion,