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The victim, identified as David James Bueche, was assaulted by four men as he was looking for his accommodation in Johannesburg's affluent Sandton area late Wednesday, Brig. Sally De Beers said.
Following the assault, Bueche entered a house and the occupants called paramedics. They discovered he had a gunshot wound, De Beers said. The victim had complained of chest pain, but was not aware of the wound, she said.
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Bueche's condition is stable but he will remain hospitalised for up to 10 days, said Mande Toubkin, a spokeswoman for Netcare Sunninghill Hospital.
Bueche flew into the country from Los Angeles, and told the investigators that he was not here for the ongoing World Cup.
South Africa's high crime rate has been a concern since the country was awarded the World Cup bid, and officials have stressed they are doing all they can to keep World Cup visitors safe.
South Africa has one of the world's highest murder rates, with at least 50 people killed each day.
The shooting is a reminder of dangers still facing hundreds of thousands of fans here to watch the tournament.
