The English-born goalkeeper, who plays for Charlton Athletic in League One, fractured a finger during the warm-up at Burton Albion last weekend and will not play again for at least six weeks.
The injury came just hours after his rival for the number one jersey in the Ghana side, Richard Ofori (29), had been ruled out with a knee problem, leaving the Black Stars with a goalkeeping crisis.
Third choice Lawrence Ati-Zigi (25), who plays at St Gallen in Switzerland, will take over but Wollacott will be on hand to offer support after successful surgery.
“He had an operation which has gone very well and now it’s the rehabilitation process,” said Charlton manager Ben Garner on the club’s website on Saturday.
“There’s not much you can do really; it will just be a case of splinting it and keeping it mobile.
“He’s still due to go out and join Ghana and have that experience. He’s been a key part of them getting there so he fully deserves to go and be out there with the squad and experience the highs and lows of a World Cup.”
Garner said Wollacott, who started out at his hometown club Bristol City but made his league breakthrough at Swindon Town, had been denied a wonderful opportunity.
“I was so disappointed for him over the weekend and for a good couple of days if I’m honest. Having seen Jojo’s progression over the last 16 months or so, it’s been incredible. The talent was there, he just needed the opportunity and he’s taken those opportunities with both hands.
“He’s had a fantastic season in League Two, he’s become Ghana’s number one, he’s had a really strong start to life in League One here with us and then he’s about to go to the World Cup so it’s a devastating blow for him.
"What I will say knowing him is that he’s got a fantastic mentality. He will come back stronger, he will come back better and he will put the disappointment behind him and use it as fuel for the rest of his career.”
Wollacott debuted for Ghana in the World Cup qualifiers a year ago when Ofori was injured and kept goal for the Black Stars at the Africa Cup of Nations finals at the start of the year.
Ghana kick off their World Cup campaign in Group H against Portugal in Doha on Thursday.
