Pecnik came on as a second half substitute and was carried off on a stretcher in injury time after a collision with an opponent in the Group C match at Ellis Park.
"Pecnik was taken to hospital immediately and the scan revealed a fractured ankle and ligament damage, meaning that he will return to Slovenia as quickly as possible," Matjaz Vogrin told the Slovenian Football Association website.
"After additional scans, a decision will be made whether he needs to unedrgo surgery or not," he added.
Defender Marko Suler is also doubtful for Wednesday's match with England in Port Elizabeth after bruising his ribs in a physical battle with U.S. striker Jozy Altidore.
"Suler landed awkwardly on his chest following one of many duels with Altidore but fortunately he has not fractured anything," said the team's technical manager Bostjan Gasser.
Coach Matjaz Kek is again likely to use a 4-4-2 formation with Milivoje Novakovic and Zlatan Ljubijankic up front, with Valter Birsa and Andraz Kirm on either flank against England.
Slovenia, who are top of the group with four points, are looking to reach the second round in their third major tournament as an independent nation, having failed to win a match in early exits at Euro 2000 and the 2002 World Cup.
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