Robertson suffered the injury in last week's 34-19 win over the Brumbies in Perth.
The 28-year-old has been a standout player for the Force this season, and his hot form was rewarded when he was selected for Wallabies coach Eddie Jones' first training camp last month.
But Robertson's hopes of appearing in the September-October World Cup in France are now over after scans confirmed an ACL tear.
"The timing is really bad. He was playing some of his best rugby," Force coach Simon Cron said.
"We love him. Throbba is a big part of our team. He's a great man.
"He covers loosehead and tighthead. It's a big loss. But he's pretty strong, and he'll get through it."
Robertson's Force teammate Izack Rodda will take a major step towards proving his own fitness for the World Cup when he makes his return from a foot injury in Friday night's clash with the Melbourne Rebels.
Rodda re-injured his troublesome right foot during the Force's pre-season loss to the Fijian Drua in February.
It was the same foot Rodda needed surgery on last year, with the injury ruling him out of the Wallabies' 2022 international season.
The 26-year-old will make his return via the bench against the Rebels, with a successful comeback putting him back on track for the World Cup.
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