Captain Hooper limped out of Australia's defeat to Ireland in the final Test in Sydney on Saturday and is not expected to play any further part in the regular Super Rugby season.
"I know our physios are working with the Wallabies physios around the time frames and from what I understand it's minimum this stage four weeks," said Waratahs forwards coach Cron.
"We'd hope to have him back in our finals series ideally. It's very early, so they'll keep working through it."
