He has been replaced by opening batter Hazratullah Zazai
Morgan was practising with his teammates at the Ageas Bowl in Southampton ahead of Saturday's unofficial World Cup warm-up against Australia when he took a blow during catching drills.
"Eoin Morgan took a knock to his left index finger fielding this morning. He is going to hospital after practice for a precautionary X-ray," said a brief statement from the ECB.
Morgan, 32, was one of 14 players preparing at Hampshire's ground, with Joe Root absent on personal business.
England have climbed to the top of the one-day international rankings under the leadership of Morgan, who is also a key member of their powerful batting line-up.
The host nation play the opening match of the World Cup against South Africa on May 30.
He has been replaced by opening batter Hazratullah Zazai
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