The youngster was taken to hospital after suffering a head injury in defeat to Fulham on Sunday.
George is back home and we will continue to monitor him over the coming days as he completes the graduated return to play programme," said West Ham performance director Richard Collinge.
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After the game, Irons manager David Moyes said: I am really disappointed for George.
He has been doing really well in training, done really well for the 21s. He started well with the ball, had some really nice touches.
He is a terrific footballer, a great little technician."