Injured Petric out until next year
The loss of Petric will be a big blow to Croatia, who play their remaining World Cup qualifier away to Kazakhstan on October 14 after warming up with a friendly against Qatar.
Hamburg said Petric would have the operation on Wednesday after suffering an injury during Sunday's 3-1 win at Hertha Berlin.
"Petric will be absent from the HSV team until the end of the first half of the championship (Bundesliga)," Hamburg doctor Oliver Dierk told the club's website.
Croatia, who host Qatar on Thursday, are second in European Group Six with 17 points from nine games and just the Kazakhstan match remaining.
They are two points ahead of Ukraine, who have a game in hand and host England on Saturday.
England have already won the group and qualified for South Africa. The best eight runners-up in the nine European groups play off in November for four more places in South Africa.
Hamburg are second in the Bundesliga behind Bayer Leverkusen on goal difference. They are already missing Peru striker Paolo Guerrero, who is expected to be out for six months with a knee injury.