Along with Ashwin, two other overseas players' contracts were also cancelled.
Ashwin had signed up with the club in January and was expected to play in the majority of matches in the county championships. It would have been the 33-year-old's third county stint, having represented Worcestershire and Nottinghamshire in the past.
The club also terminated contracts of two overseas players, South African spinner Keshav Maharaj and West Indies batsman Nicholas Pooran.
"Firstly, I really appreciate the players' understanding in this matter. We have been in regular contact with the players and their agents throughout this Covid pandemic. They have been extremely professional and appreciate the uncertainty facing counties at present," Yorkshire's Director of Cricket, Martyn Moxon said.
"We hope that we will be able to see them at Emerald Headingley in the future," he added.
(PTI inputs)