Gloucestershire's Lewis - who has not played in the tournament proper - is set to return home to be with his wife, who is experiencing complications in pregnancy, an England spokesman said.
Broad, 20, has played five one-day internationals since making his England debut last year.
The son of former England opening batsman Chris and the current Young Cricketer of the Year in England, Leicestershire's Broad was involved in England A's recent tour of Bangladesh.
He's previously been involved in England's Academy squad, which was based in Perth during the senior side's 5-0 Ashes thrashing in Australia.
England's chairman of selectors, David Graveney, said in a statement: "We fully understand Jon's need to be with his wife at this time and we are grateful to the (World Cup) Technical Committee for approving our request for a replacement player.
"Stuart Broad performed well with the Academy squad in Australia and on England A's recent tour of Bangladesh and I am sure he will be thrilled to be joining up with the squad in the Caribbean."
Lewis, 31, was one of six players fined for staying out late drinking following England's six-wicket defeat by New Zealand in their opening Group C match in St Lucia.