Smith suffered the injury while attempting to prevent Leeds striker Billy Sharp from scoring a late winner in the West Yorkshire derby, and he required lengthy treatment on the pitch before leaving the field on a stretcher wearing an oxygen mask.
Huddersfield subsequently released a statement on their official Twitter account, posting: "#htafc confirms Tommy Smith has been airlifted by Yorkshire Air Ambulance to Leeds General Infirmary for tests after suffering a head injury.
"The club will give further updates on Tommy Smith when we have further news from the hospital."
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