Topley fractured his left index finger during the defending champions' 229-run loss to South Africa in Mumbai on Saturday, their second defeat in a row.
Carse, whose last international appearance was against Ireland in September, joins an England team struggling at the ninth place on the table after just one win in four matches.
England coach Matthew Mott said they still stood a chance to make a comeback.
"There’s a lot that has to go our way now, but we’re still in there," Mott told reporters in Bengaluru on Sunday.
"We’ll keep throwing punches. I still think we can win this tournament."
The England players were down in confidence after the losses but needed support from the management, Mott added.
"They’re hurting. They’re bloody good players, there’s no doubt about that. You don’t lose that, but you can lose your confidence,” he said.
