Smith, a 22-year-old defender, was knocked unconscious and had to be taken off the pitch on a stretcher late in the Championship game after a collision with his own goalkeeper Joe Murphy.
Huddersfield reported on their official website later on Saturday that Smith had undergone scans and tests, was in a stable condition but would stay overnight at Leeds General Infirmary.
"We are pleased to report Tommy has been sitting up and talking to members of Huddersfield Town's staff who have visited him on Saturday evening," the website reported.
Smith was treated for nine minutes before being given oxygen and taken off the field.
Straight after the game, officials were still so concerned about his condition that they organised an air ambulance helicopter to land on Huddersfield's John Smith's Stadium pitch to fly Smith to hospital in nearby Leeds.
(Writing by Ian Chadband, editing by Pritha Sarkar/Alan Baldwin)
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