According to the ICC's playing conditions for the World Cup, substitute fielders are not permitted from outside the 15-man playing squad, although those rules do not apply to the warm-up games.
Morgan suffered a small fracture when he was struck on the index finger of his left hand before heading to hospital for a precautionary x-ray.
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.
World Cup rules permit a replacement player to be drafted into the team but the injured player can not return to the 15-man squad.
England will be the guests for the first part of the summer from mid-December until mid-February and will play four Test matches, three One-Day Internationals and three T20 International matches.
"I think the thing with a broken finger is that it hurts a lot in the nets but once you get out in the game with the adrenalin going it's not too much of an issue normally". "England captain Eoin Morgan has sustained a small flake fracture to his left index finger".
And the captain expects to be fit for the start of the tournament when England face South Africa at the Oval on Thursday.
Morgan has been a stupendous leader for England following the dismal performances in the ICC Cricket World Cup 2015. The 32-year-old left-hand batsman is in a good form, scoring two half-centuries in the recent ODI series against Pakistan that England won 4-0. Morgan can also play shots as and when required which makes him a crucial campaigner for England.