Dhawan sustained the injury against Australia but continued to play on, scoring a match-winning century. However, he did not take the field for the second innings.
Assistant coach Sanjay Bangar had said last week that they would make a call on Dhawan's injury after he was rested against New Zealand and Pakistan but the BCCI said his hand would need to remain in a cast until the middle of July.
"Shikhar Dhawan has been diagnosed with a fracture of the first metacarpal on his left hand following a ball impact injury during the team's second match versus Australia at the Oval on 5th June 2019," BCCI said in a statement.
"Following several specialist opinions, he will remain in a cast until the middle of July and therefore will not be available for the remainder of the World Cup."
Wicketkeeper-batsman Rishabh Pant, who was flown in as a cover and joined the team before Sunday's victory against Pakistan, is set to be named as Dhawan's replacement.
India play Afghanistan next on Saturday at The Rose Bowl.