Jedinak was substituted in the 59th minute of Palaces season-ending 2-2 draw with Fulham on Sunday.
The 29-year-old is expected to be out for three weeks, however, the midfielder was pleased with the results of a scan and expects to be ready in time for the finals in Brazil next month.
Its a little bit sore and its going to mean I miss a couple of weeks or so, but I just got the scan results back and honestly the news is probably as good as I could have hoped for, Jedinak told The Daily Telegraph.
The doctors say Im looking at two to three weeks, so I have to concentrate now on doing everything in my power to be ready in that timeframe.
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 Im seriously glad I did come off now.
Jedinak may join the Australia training camp late as a result of the injury, though is expected to be named as national captain when he does arrive in Lucas Neills expected absence.
However, the former Central Coast Mariners man is not yet entertaining thoughts of leading his country on the world stage.
Im definitely coming back to Australia at some point in the next couple of weeks, he added. The club and the national team staff are just working out the details now of exactly what the rehab will be.
Ive not heard anything (over the captaincy), and its 100 per cent a decision for the manager and what he thinks is appropriate. If that involves me then of course it would be a huge honour, but itll be whats 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 its a special feeling.
Australia take on Chile in their opening Group B clash on June 13 before facing the Netherlands and holders Spain.