Ashwin, who has previously played county cricket for Worcestershire and Nottinghamshire, had been due to play the majority of the County Championship season, while Pooran was set to re-join the club for the T20 Blast having played three times in the competition last summer. Maharaj had been due to play the first two games of the County Championship season.
All professional cricket in England and Wales has been suspended until July 1 at the earliest due to the Covid-19 pandemic, and several counties have now cancelled contracts for their overseas players both as a cost-saving measure and as a reflection of the uncertainties surrounding international travel.
"I really appreciate the players' understanding in this matter," said Martyn Moxon, Yorkshire's director of cricket. "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. We hope that we will be able to see them at Emerald Headingley in the future."