The Wallabies fell to a 20-16 defeat during the third-Test and subsequently conceded the series 2-1, despite winning the first meeting.
Hooper limped out of the clash with the hamstring issue at the Allianz Stadium in Sydney and he now faces a race against time to be ready for the Super Rugby playoffs.
The Waratahs flanker is expected to be on the sidelines for around four weeks, although assistant coach Simon Cron admits that timeframe could change
Cron said: "Our physios are working with the Wallabies physios around the time frames and from what I understand, at this stage, I'd say four weeks.
"We'd hope to have him back in our finals series. It's very early. They will keep working through it."