"He's ruled out of the World Cup and he's flying home tomorrow," an England spokesman said.
"We will decide about the replacement tomorrow."
Although there was no further comment available from the team immediately, a forlorn Broad had spoken to reporters earlier in the day to explain his injury.
"I think I have got a little side niggle, I'm not sure how serious it is at the moment. I had a couple of scans and am waiting for the results," Broad told a news conference earlier on Tuesday.
"I have never had a side strain in this manner before so I don't really know the symptoms.
"It's a bit sore ... but that might be just after a vigorous couple of games in a few days. It's quite a common injury for bowlers.
"If it is an actual side strain or tear, it is something you have to be very careful of and make sure you take your time to get fit and not rush back.
"But obviously, I'll be bitterly disappointed if it is the end of my World Cup," he added.
Broad's news is the second injury setback to hit England in as many days.
On Monday, batsman Kevin Pietersen [ Images ] said he was flying back home as he needed immediate attention on a hernia.
Broad was largely responsible for England's dramatic six-run win over South Africa [ Images ] on Sunday as he claimed the last two wickets in four balls to seal the win. He finished with 4-15.
The 24-year-old generated swing -- both conventional and reverse -- to torment the South African batsmen and made sure England's meagre total of 171 could not be equalled.
Hence his absence will be a big blow to England as he has been their main strike bowler, taking six wickets in three matches. He missed the game against India [ Images ] with an upset stomach.
The England team, however, was boosted by the arrival of Eoin Morgan [ Images ] in Chittagong on Tuesday as a replacement Pietersen.
Morgan, a dangerous middle-order batsman, had been withdrawn from the squad with a broken finger but Pietersen's exit earned him a recall.
"He's (Morgan's) been our best one-day batsman for the past year, he's won us games single-handedly. I know the whole squad are excited about his arrival," said Broad.
"We know what a skilful player he is and what he can add to this team, so it's a big boost to have him in the side because we know he can win games and plays spin particularly well."
England lie second in Group B with five points and with two games remaining. The top four teams from each group progress to the quarter-finals.