Inglis, reserve to regular wicketkeeper Matthew Wade in their 15-man World Cup squad, was injured when a club snapped in his hand during a "normal golf swing" while on a morning round with some of his team mates, a team spokesman said.
Australia open their title defence against New Zealand in Sydney on Saturday, a rematch of last year's final in the United Arab Emirates.
Golf has already cost England the services of Jonny Bairstow at the tournament after he was ruled out by a freak injury while playing a round in September. The batsman slipped while out on a course and needed surgery on a broken leg and dislocated ankle.