Jedinak, widely tipped to captain Australia at the June 12 to July 13 tournament in Brazil, limped off in Palace's season-ending 2-2 draw with Fulham on Sunday, sending a shudder through the Socceroos camp.
The 29-year-old had a scan and though he was feeling sore, the results were "as good as (he) could have hoped for," Jedinak said.
"The doctors say I'm looking at two to three weeks, so I have to concentrate now on doing everything in my power to be ready in that timeframe," he added.
"It came on all of a sudden in the game, just as I went to take off for a header I knew something was wrong. It was more precautionary than anything, there was no point in carrying on, and I'm seriously glad I did come off now.
"I'm definitely coming back to Australia at some point in the next couple of weeks, the club and the national team staff are just working out the details now of exactly what the rehab will be."
Until the injury, Jedinak had played every minute of Palace's successful promotion to the Premier League, helping the club stave off relegation with room to spare and earning plaudits from coach Tony Pulis and pundits.
With long-serving skipper Lucas Neill out of Ange Postecoglou's World Cup plans, Jedinak made his debut as captain for the Socceroos in their 4-3 loss to fellow World Cup finalists Ecuador in a friendly in March.
The tough-tackling midfielder will be key for Australia's slim hopes of battling through a 'group of death' that also includes Spain, Netherlands and Chile to make the knockout rounds.
Postecoglou is set to name a preliminary 30-man squad on Wednesday, with training camps to follow in Gosford, on eastern New South Wales state's Central Coast, and Sydney.
Postecoglou has been cagey on his long-term replacement for skipper Neill, who led the Socceroos in their disappointing 2010 World Cup campaign in South Africa where they bowed out in straight sets.
"I've not heard anything, and it's 100 percent a decision for the manager and what he thinks is appropriate," Jedinak said.
"If that involves me then of course it would be a huge honour, but it'll be what's right for the team.
"When the armband is given to you, the feeling in your head is just 'wow' - you think of the people who have had the honour of captaining the side before, the characters, and it's a special feeling."