Following the removal of Shikhar Dhawan, Haddin went to congratulate his teammate but was poked in the eye after Faulkner miscalculated the high-five effort, which led to him receiving treatment after slumping to the ground.
George Bailey, the Australia captain, told reporters: "How embarrassing. We couldn't even get our high-fives right.
"What about just a handshake! Just take it back to 'well bowled'."
The injury is not expected to keep him out for long but Haddin could miss Wednesday's encounter.