Reigning champions England suffered a colossal 229-run thrashing by South Africa in Mumbai on Saturday to leave their hopes of a successful title defence hanging by a thread.
Their record one-day international defeat was compounded when England coach Matthew Mott (50) confirmed Topley was unlikely to feature again at the tournament.
"We're still waiting to confirm about Reece's finger, it looks like it's a crack, that's an early diagnosis," Mott told Sky Sports.
"It's highly likely there's a fracture there, which would make it difficult for him to keep playing."
Topley, who has taken eight wickets in three games, was struck on the index finger of his bowling hand when attempting to block a drive in his follow-through
The left-arm paceman's career has been blighted by injury problems and he missed England's victorious T20 World Cup win in Australia last year following a freak accident where he tripped on a boundary sponge on the eve of the tournament.
On Saturday, he returned to the attack and managed to dismiss Aiden Markram and David Miller.
But he was not at his best and eventually conceded 88 runs from his 8.5 overs as Heinrich Klaasen and Marco Jansen ran riot while powering the Proteas to a huge total of 399-7.
Archer, one of the stars of England's 2019 World Cup triumph, joined the squad earlier this week but the fast bowler has not played competitively since May.
His time in India is being seen by England primarily as a chance for their medical staff to assess Archer's progress as he continues to recover from a longstanding elbow injury.
"Jofra Archer is not going to be considered for selection," said Mott.
England are able to call up injury replacements, with Brydon Carse (28) a potential option.
