Gunnarsson suffered the injury during a recent international game for Iceland against Slovenia and it was initially feared that he could be sidelined for three months, casting his availability for the club's Premier League debut into doubt.
Cardiff boss Malky Mackay does not yet know for certain when Gunnarsson may be able to return to action but he is confident about the 24-year-old's recovery.
"We think Aron will be okay for the start of the season," Mackay said in the Daily Star.
"We should have a much clearer picture next week."
Gunnarsson also eased fears of a long lay-off, tweeting: "Thanks for all the messages. I am okay and will be alright."
Mackay will be buoyed by the news that Gunnarsson should be fine for the start of the new season as he was a key player in Cardiff's promotion-winning campaign, featuring in all but one of their 46 Championship games.