The batsman, fielding with a helmet, was standing in an unusually advanced slip position when he could not hold on to a fast-travelling edge from South Africa captain Temba Bavuma, who had only made two at the time.
After on-field attention, Smith left the field - evidently in pain - with South Africa then 76-2 chasing 282 to win on the third day.
A Cricket Australia statement said: "Steve Smith has suffered a compound dislocation of his right little finger while fielding in the slip cordon during the ICC Men's World Test Championship final against South Africa at Lord's.
"He was assessed by Australian team medical staff at the ground and taken to hospital for X-rays and further treatment."
Smith has scored more than 10,000 Test runs at a superb average of more than 56.
The 36-year-old former Australia captain made a valuable 66 in the WTC title-holders' first innings at Lord's.
His injury will be a concern to Australia ahead of their three-Test series away to the West Indies, starting in Barbados on June 25.