The 32-year-old managed to send the ball back across the boundary in mid-air but hit his head on the turf as he landed and was taken away by medical staff.
"Steve Smith has a concussion and will be subject to low-level protocols for the next few days and full recovery in 6-7 days. He will miss the remainder of the T20 International Series against Sri Lanka," the official handle of Cricket Australia tweeted.
Australia have taken a 2-0 lead in the five-match series and the third T20I will now be played on Tuesday.
