The 23-year-old signed a long-term deal with the Gunners on Monday after the north London club agreed a £16m fee with Manchester United.
Welbeck is currently preparing for England’s friendly against Norway at Wembley on Wednesday night.
But Hodgson confirmed that the forward had suffered a setback in training late on in Tuesday’s session.
Asked about Welbeck’s move to Arsenal, Hodgson said: “We are happy for Danny.
“He felt the move might lead to more regular football and that will only be to our advantage and we think or hope he will be ready to start for Arsenal.
“But unfortunately in training today he did manage to receive a knock in the session, but I have been assured he is OK and that it will not rule him out, but obviously I suppose it could happen.
“I would be very disappointed if he could not play tomorrow because of what happened with the last kick of the session.”
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