Groves has been training with the Royal Marines in Plymouth, on Britain's south-west coast, for the fight which is expected to take place in August or September.
The 27-year-old, who was knocked out by Carl Froch in the WBA and IBF super-middleweight title fight last year, was taken to hospital for his injury but was released.
"We can confirm that a minor incident took place on Monday afternoon as part of his preparation for his forthcoming WBC super-middleweight world championship fight with Badou Jack scheduled to take place in the United States in late August or early September," Groves' management Sauerland Promotions said in a statement.
"George was taken to hospital for precautionary checks but immediately released following the incident that took place while taking part in a boat activity with the Marines. The injury will not affect his preparations for the Jack fight and he will continue his training camp as planned."
(Reporting by Pritha Sarkar; Editing by Frank Pingue)
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