The £8 million club-record signing from FC Copenhagen is suffering with an ankle injury sustained in training.
He was absent for Cardiff's 1-0 pre-season win over Chievo on Saturday and manager Malky Mackay confirmed that the 20-year-old may miss the first game of the campaign against West Ham at Upton Park.
|100/1||Andreas Cornelius is 100/1 with BetVictor to be the Premier League's top scorer
Jordon Mutch, Joe Mason and Craig Bellamy also missed the victory over the Serie A side, although the trio's injuries are not thought to be serious.
"Jordon had a problem with his groin in the warm up with 15 minutes to go, it's not too serious," Mackay confirmed to the club's official website.
"Joe Mason rolled his ankle during the week against Port Talbot and Craig Bellamy was ill overnight so again, short-term things."
Meanwhile, Kim Bo-Kyung, who joined Cardiff from Japanese side Cerezo Osaka last year, has been in fine form in pre-season, scoring against Chievo, and Mackay hopes that can continue when the Premier League season starts.
"It's something we wanted to add in terms of the all round make-up of his game," Mackay told the club's official website as he reflected on the victory over the Italians.
"He [Kim] showed some sublime touches, but again got on the scoresheet which is important for him in his slightly different role.
"He's only young, you've got to remember that - and coming in from a completely different culture and language, his English has improved massively over the year.
"As the season went on [last year] you saw how he got to grips with the Championship, understood the type of football that it was and I think we saw the improvement as the year went on. I knew about the raw talent the boy had, it was about giving him time to settle."