The Middlesex captain was hit in the back of the head by a ball thrown to the stumps by a substitute fielder and missed by wicketkeeper John Simpson during the match against Hampshire at Southampton's Rose Bowl.
Voges had to be helped from the ground by physios and had likely suffered concussion, Middlesex said.
“It is sad for Adam and disappointing for us as we will have no more use out of him in this match," Middlesex managing director of cricket Angus Fraser said.
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“He wasn’t feeling very well in the dressing room so we decided to get him to the hospital to get him checked over."
Cricket Australia were monitoring the situation.
Australian cricket was plunged into mourning in 2014 when test batsman Phillip Hughes was struck in the head by a ball in a domestic game and subsequently died in hospital at the age of 25.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
