The 34-year-old, who has won 49 caps, sustained the injury in training for his Spanish club Sevilla and the initial scan revealed he would be out for the rest of the season at least.
"The preliminary result does not look good, he will undergo further examinations but as things stand now it is unlikely he will recover in time for the World Cup finals," Serbian Football Federation (FSS) spokesman Aleksandar Boskovic told Reuters on Thursday.
"Of course we are hoping he will be fit because players can sometimes come back from injury more quickly than expected but it is a slim chance."
Dragutinovic was an automatic starter for Serbia at left-back and centre-back in their unsuccessful Euro 2008 qualifying programme but lost his place for the World Cup campaign that followed.
Lazio's Aleksandar Kolarov has become first choice left back and Real Zaragoza's Ivan Obradovic, who has recovered from a knee injury, has plenty to offer as cover.
The Serbians also have a plethora of players to choose from in the centre of defence, led by Manchester United's Nemanja Vidic and Udinese regular Aleksandar Lukovic.
Their Group D rivals in the June 11-July 11 tournament in South Africa are Germany, Australia and Ghana.
