Writing on Twitter, Richard said the site would shut at the end of the year or early January.
He added that the restaurant hadn’t “gone bust” but the couple completed their lease several months ago and were now pursuing an “exciting opportunity”.
Rascills opened in the village of Raskelf in autumn 2016 and is recommended in the Michelin Guide and Good Food Guide.
The Johns' are the only members of staff, with Richard cooking and Lindsey serving front of house.
The couple previously ran award-winning restaurant Artisan in Hessle from 2004-2013.
They took on The Falcon Pub in Withernwick in 2014 but left in 2016 to help their friend Andrew Pern set up his York restaurant, before opening Rascills.
Many thanks for all the messages of support. You certainly find out who your friends are in this industry. Can I just say we haven't gone bust etc. We completed our lease several months ago & are now pursing an exciting opportunity. Hopefully all goes to plan! More info to come— Rascills (@Rascills) October 9, 2018